http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=KaimaiPhysics Book - User contributions [en]2026-04-30T09:02:18ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40741Quantum Theory2022-07-25T00:29:07Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
<br />
1922 - Arthur Compton discovered the Compton effect.<br />
<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
<br />
1930 - Paul Dirac postulated positrons.<br />
<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
[[File:Electron_Spin_(I_made_this!).jpg]]<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity. <br />
<br />
Spin quantum numbers describe the angular momentum of electrons. The electron rotates around the axis and has both angular momentum and orbital angular momentum. And because one orbit can only hold two electrons, one electron is positive 1/2 and the other is -1/2<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40727Quantum Theory2022-07-24T20:50:04Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
<br />
1922 - Arthur Compton discovered the Compton effect.<br />
<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
<br />
1930 - Paul Dirac postulated positrons.<br />
<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
[[File:Electron_Spin_(I_made_this!).jpg]]<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40726Quantum Theory2022-07-24T20:49:23Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
<br />
1922 - Arthur Compton discovered the Compton effect.<br />
<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
<br />
1930 - Paul Dirac postulated positrons.<br />
<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
[[Electron_Spin_(I_made_this!).jpg]]<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=File:Electron_Spin_(I_made_this!).jpg&diff=40725File:Electron Spin (I made this!).jpg2022-07-24T20:48:31Z<p>Kaimai: </p>
<hr />
<div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40724Quantum Theory2022-07-24T20:42:24Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
<br />
1922 - Arthur Compton discovered the Compton effect.<br />
<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
<br />
1930 - Paul Dirac postulated positrons.<br />
<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40723Quantum Theory2022-07-24T20:41:44Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
1922 - Arthur Compton discovered the Compton effect.<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
1930 - Paul Dirac postulated positrons.<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40722Quantum Theory2022-07-24T20:41:12Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
1900 - Max Planck proposed Planck's radiation law to explain the radiation emission of blackbody. He also proposed the quantization of photons, which is now known as the equation e=h ν。 Therefore, quantum mechanics was born.<br />
1902 - Hendrick Lorentz explained the Zeeman effect through Lorent's ether theory.<br />
1905 - Albert Einstein explained the photoelectric effect. He regarded light as particles, so he advocated Newton's particle theory. He also introduced the special theory of relativity to the world.<br />
1909 - Ernst Rutherford α The concept of atomic nucleus is proposed in the X-ray scattering experiment (also known as the gold foil experiment).<br />
1909 - Geoffrey Taylor proved the formation of single photon interference mode, which rekindled the Newton Huygens debate for more than two centuries.<br />
1913 - Johannes stark discovered the Stark effect, an electric field phenomenon similar to the Zeeman effect.<br />
1913 - Niels Bohr introduced his atomic model and put forward the theory of quantifying atomic radius.<br />
1915 - Einstein proposed general relativity and Einstein's field equations (see quantum field theory).<br />
1916 - Einstein theoretically pointed out that Planck's energy quantum has particle like momentum.<br />
1916 -- Arnold Sommerfeld proposed the concept of atomic sub shell, which extended Bohr's atomic theory.<br />
1918 - Ernst Rutherford discovered protons (and coined the word) in atoms.<br />
1921 - Theodore Kaluza published Kaluza theory (the first theory related to quantum field theory).<br />
After the previous discoveries and the sudden prosperity of scientific discoveries led by quantum and relativity, the formalization of quantum mechanics, a new field of physics, has become clear. Bohr, Heisenberg and Schrodinger began to develop this formalization in the 1920s, and soon Max Born, Paul Dirac and John von Neumann joined the ranks.<br />
1922 - Arthur Compton discovered the Compton effect.<br />
1922 - Otto stern and Walter graher conducted the stern graher experiment, which proved the quantification of spin.<br />
1923 - Louis de Broglie assumed wave particle duality and de Broglie wavelength λ= h/mv。<br />
1924 - Wolfgang Pauli explained the fine structure of spectral lines with the concept of internal angular momentum of electrons.<br />
1925 - George Ulenbeck and Samuel goodschmidt proposed the existence of electron spin.<br />
In 1925, Heisenberg, born and Pascal Jordan proposed the matrix mechanics expression of quantum physics.<br />
1925 - Frederick hund theoretically proposed the principle of maximum multiplicity in atoms, which is now known as the hund rule.<br />
1926 - Erwin Schrodinger proposed the Schrodinger wave equation, which is the most important equation in quantum mechanics.<br />
1926 - Oscar Klein explains the Kaluza hypothesis (one of the earliest ideas about quantum gravity) by integrating the quantum mechanics created by Heisenberg and Schrodinger.<br />
1927 - Werner Heisenberg published an article introducing Heisenberg's uncertainty principle: Δ p· Δ x≥h/4π。<br />
1927 - Solvay conference, proposed the Copenhagen interpretation of quantum mechanics.<br />
1928 - Paul Dirac established the Dirac equation of quantum mechanics.<br />
1929 - Oscar Klein predicted the Klein paradox, the quantum tunneling effect.<br />
1930 - Paul Dirac postulated positrons.<br />
1930 - Paul Dirac proposed hole theory (also known as Dirac sea model).<br />
1932 - John von Neumann described the mathematical basis of quantum mechanics from the perspective of Hermite operators and linear algebra.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40721Quantum Theory2022-07-24T20:22:49Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40720Quantum Theory2022-07-24T20:22:17Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
[[File:0824ab18972bd40791c9d4c870899e510fb309fc.webp]]<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=File:0824ab18972bd40791c9d4c870899e510fb309fc.webp&diff=40719File:0824ab18972bd40791c9d4c870899e510fb309fc.webp2022-07-24T20:21:07Z<p>Kaimai: spin of electrons</p>
<hr />
<div>== Summary ==<br />
spin of electrons</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40718Quantum Theory2022-07-24T20:14:47Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40717Quantum Theory2022-07-24T20:12:55Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Kaimai Shi Summer 22===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40716Quantum Theory2022-07-24T20:12:26Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Chris Allen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==Intro to Spin(Electrons)==<br />
what is spin of electrons in Quantum Mechanics<br />
<br />
One of the basic properties of electrons. The abbreviation of electron intrinsic motion or quantum number of electron intrinsic motion. In 1925, inspired by the Pauli exclusion principle, G.E. Ulenbeck and S.A. guzmitt analyzed some experimental results of atomic spectroscopy and proposed that electrons have intrinsic motion - spin, and have spin magnetic moments associated with electron spin. This can explain the fine structure of atomic spectra and the abnormal Zeeman effect. Where electron spin s= 1/2. In 1928, p.a.m. Dirac proposed the relativistic wave equation of electrons, which naturally includes electron spin and spin magnetic moment. Electron spin is a quantum effect, which cannot be understood classically. If we regard electron spin as rotation around an axis, we will get a result that is contradictory to relativity.<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40715Quantum Theory2022-07-24T19:54:45Z<p>Kaimai: /* Particle Spin */</p>
<hr />
<div>===Claimed by Chris Allen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==Spin(Electrons)==<br />
what is spin in Quantum Mechanics(what is and why are Electrons Spin1/2)<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40714Quantum Theory2022-07-24T19:53:58Z<p>Kaimai: /* The Main Idea */</p>
<hr />
<div>===Claimed by Chris Allen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==Particle Spin==<br />
what is spin in Quantum Mechanics(what is and why are Electrons Spin1/2<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40713Quantum Theory2022-07-24T19:51:32Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Chris Allen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==The Main Idea==<br />
Particle spin<br />
<br />
<br />
<br />
<br />
<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40712Quantum Theory2022-07-24T19:32:36Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Chris Allen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Tunneling_through_Potential_Barriers&diff=40711Quantum Tunneling through Potential Barriers2022-07-24T19:28:15Z<p>Kaimai: /* History */</p>
<hr />
<div>'''Page Claimed By: Shreenithi Katta Spring 22'''<br />
<br />
'''Quantum tunneling''' is a phenomenon of quantum mechanics in which a wave function can travel through a potential barrier and be observed on the other side. It utilizes the [[Heisenberg Uncertainty Principle | Heisenberg uncertainty principle]] and the [//en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] to explain the classically forbidden phenomenon. Using these principles, the probability that a particle can tunnel through a potential barrier can be calculated.<br />
<br />
==Main Idea==<br />
A potential barrier can be defined as a bounded region of significantly high potential than the space it is surrounded by. For the purpose of quantum tunneling, the potential barrier is finite with a specified height, width, and some unknown potential defined in terms of the particle that is incident upon it (<math> V_0 > E </math>).<br />
<br />
===Classical Theory===<br />
According to classical mechanics, a particle of energy <math>E</math> does not have sufficient energy to pass through the barrier of energy <math> V_0 > E </math> - the particle is classically forbidden to enter the region. However, due to the [[Wave-Particle Duality]], quantum mechanics predicts that the wavefunction of the particle has a chance of entering the classically forbidden region.<br />
<br />
===Quantum Theory===<br />
====Wave Mechanics====<br />
Wave mechanics tells us that when a wave travels through a medium are partially absorbed, transmitted, and reflected. With a finite potential barrier of certain dimensions, we can create three regions the wave function travels through i) the initial region before the potential barrier ii) the finite potential barrier iii) the region after the potential barrier. Using the wave properties, we know a portion of the incident wave function is reflected, absorbed, and transmitted into region B where the same happens on the border of regions II and III.<br />
<br />
====Heisenberg Uncertainty Principle====<br />
The [[Heisenberg Uncertainty Principle | Heisenberg uncertainty principle]] can be used to explain quantum tunneling a bit more intuitively. The second uncertainty principle outlined by Heisenberg is concerned with energy and time. Given a short amount of time to examine a particle, the uncertainty in the energy it contains vastly increases. Applying that to this phenomenon is simple. If the uncertainty in the energy of the particle is great in a short amount of time, there is a possibility that the particle contains enough energy to enter the classically forbidden region. Whether it is reflected halfway through or transmits to the other side, the uncertainty in the energy essentially allows for a classical particle to exist in a potential barrier. <br />
<br />
====The Schrödinger Equation====<br />
The [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] tells us that a wave function must be continuous at each boundary it encounters, and the derivative of the wave function must also be continuous except when the boundary height is infinite. Applying this to a finite potential barrier, we can find the probability a particle can tunnel through a potential barrier. Notably, the wave functions and calculations most resemble the [[Solution for a Single Particle in a Semi-Infinite Quantum Well | solution for a single particle in a semi-infinite well]] when <math>V_0 > E </math> in regions II and III. <br />
<br />
===Mathematical Model===<br />
Beyond the conceptual understanding of how quantum tunneling works, calculations can be made to determine the probability a wave function can tunnel through a specific finite potential barrier. This is known as transmission probability and to understand this equation, we must look at the wave equations associated with the potential barrier.<br />
<br />
====Wave Equations====<br />
The time independent Schrodinger equation is given by the following equation.<br />
<br />
<math>-\frac{\hbar^2}{2m}\frac{d^2 \psi(x)}{dx^2} + V(x)\psi (x) = E \psi(x)</math><br />
<br />
As mentioned before, the finite potential barrier creates three different regions with their own unique wave equations. Let's assume that the potential barrier is from <math>0 \le x \le L</math>. Given that, we can define the potential as follows: <br />
<br />
<math> V(x) = \begin{cases} <br />
0 & x < 0 \\<br />
V_0 & 0\leq x\leq L \\<br />
0 & x> L <br />
\end{cases} </math><br />
<br />
Thus, we can write the Schrodinger equations for the three regions.<br />
<br />
* '''''Region I''''' : <math> -\frac{\hbar^2}{2m}\frac{d^2 \psi(x)}{dx^2} = E \psi(x) </math><br />
<br />
* '''''Region II''''' : <math> -\frac{\hbar^2}{2m}\frac{d^2 \psi(x)}{dx^2} + V_0 \psi (x) = E \psi(x) </math><br />
<br />
* '''''Region III''''' : <math> -\frac{\hbar^2}{2m}\frac{d^2 \psi(x)}{dx^2} = E \psi(x) </math><br />
<br />
Boundary conditions require that the wave functions and their derivatives are continuous on each boundary i.e <math> x = 0 </math> and <math> x = L </math>. The general solution for each region, <br />
<br />
* '''''Region I''''': <math> \psi(x)_I = Ae^{ikx} + Be^{-ikx} </math><br />
<br />
* '''''Region II''''': <math> \psi(x)_{II} = Ce^{-\alpha x} + De^{\alpha x } </math><br />
<br />
* '''''Region III''''': <math> \psi(x)_{III} = Fe^{ikx} + Ge^{-ikx} </math><br />
<br />
where <math> \alpha = \sqrt {\frac{2m}{\hbar^2} (V_0 - E)} </math> and <math> k = \sqrt {\frac{2m}{\hbar^2} E} </math>. <br />
<br />
There is only one direction in which the wave in region III is traveling (<math> +\infty </math>). Thus the wave functions are now, <br />
<br />
* '''''Region I''''': <math> \psi(x)_I = Ae^{ikx} + Be^{-ikx} </math><br />
<br />
* '''''Region II''''': <math> \psi(x)_{II} = Ce^{-\alpha x} + De^{\alpha x } </math><br />
<br />
* '''''Region III''''': <math> \psi(x)_{III} = Fe^{ikx} </math><br />
<br />
It is important to note that the constants A, B, C, D, and F refer to the amplitude of the five waves in this problem:<br />
* A: incident wave at <math> x = 0 </math><br />
* B: reflected wave at <math> x = 0 </math><br />
* C: incident wave at <math> x = L </math> <br />
* D: reflected wave at <math> x = L </math> <br />
* F: transmitted wave<br />
<br />
====Tunneling Probability====<br />
The probability that a particle can tunnel through a potential barrier utilizes the wave functions discussed in the previous section. Specifically, tunneling probability is the ratio of the transmitted wave intensity <math> |F|^2</math> and the incident wave intensity <math> |A|^2 </math>. To solve for these constants, we must apply boundary conditions.<br />
<br />
At <math> x = 0 </math>, we know region I and II must agree and create a continuous wave function.<br />
<br />
<math> Ae^{ikx} + Be^{-ikx} = Ce^{-\alpha x } + De^{\alpha x} </math><br />
<br />
<math> \frac{d}{dx}(Ae^{ikx} + Be^{-ikx} = Ce^{-\alpha x } + De^{\alpha x}) </math><br />
<br />
<math> ik(Ae^{ikx} - Be^{-ikx}) = \alpha(-Ce^{-\alpha x } + De^{\alpha x}) </math><br />
<br />
The same applies at <math> x = L </math>.<br />
<br />
<math> Ce^{-\alpha x } + De^{\alpha x} = Fe^{ikx} </math><br />
<br />
<math> \frac{d}{dx}(Ce^{-\alpha x } + De^{\alpha x} = Fe^{ikx}) </math><br />
<br />
<math> \alpha(-Ce^{-\alpha x } + De^{\alpha x}) = ikFe^{ikx} </math><br />
<br />
After some lengthy algebra and calculations, we know that the ratio of the transmitted wave amplitude and incident wave amplitude is this messy expression.<br />
<br />
<math><br />
\frac{F}{A} = \frac{e^{-ikL}}{cosh(\alpha L) +i(\gamma /2)sinh(\alpha L)} </math>[https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.07%3A_Quantum_Tunneling_of_Particles_through_Potential_Barriers]<br />
<br />
where <math> \gamma = \frac{\alpha}{k} - \frac{k}{\alpha} </math>.<br />
<br />
We know that tunneling probability is a ratio of intensity. So when we multiply the ratio of amplitudes by the conjugate, we get the following equation for tunneling probability. <br />
<br />
<math> T \approx 16 \frac{E}{V_0} (1-\frac{E}{V_0}) e^{-2kL} </math><br />
<br />
where,<br />
<math> k = \sqrt {\frac{2m(V_0-E)}{\hbar^2}} </math> and L is the width of the barrier.<br />
<br />
===Computational Model===<br />
The following simulation illustrates a wave function for various potentials in both plane wave and wave packet form. <br />
<br />
<iframe src="https://phet.colorado.edu/sims/cheerpj/quantum-tunneling/latest/quantum-tunneling.html?simulation=quantum-tunneling"<br />
width="800"<br />
height="600"<br />
allowfullscreen><br />
</iframe> [https://phet.colorado.edu/en/simulations/quantum-tunneling]<br />
<br />
==Examples==<br />
===Simple===<br />
<br />
A particle has 5.0 eV of energy. What is the probability that it will tunnel through a potential barrier of 10.0 eV with a width/thickness of 1.00 nm?<br />
<br />
'''''Solution'''''<br />
<br />
First, let's define the given variables and equation we must use<br />
* <math> E = 5.0 eV </math><br />
* <math> V_0 = 10.0 eV</math><br />
* <math> L = 1.00 nm = 1.00 \times 10^{-9} m </math><br />
<br />
*<math> T \approx 16\frac {E}{V_0} (1-\frac{E}{V_0})e^{-2kL} </math><br />
* <math> k = \sqrt{\frac {2m(V_0 -E)}{\hbar^2}} </math><br />
<br />
Next, plug in our given values into the equation and solve.<br />
<br />
<math> k = \sqrt {\frac {2(9.11 \times 10^{-31} kg)(10.0-5.0 eV)(1.602 \times 10^{-19} J)}{(1.055 \times 10^{-34})^2}} = 1.145 \times 10^{10} m^{-1} </math><br />
<br />
<math> T \approx 16\frac {5.0}{10.0} (1-\frac{5.0}{10.0})e^{-2(1.145 \times 10^{10} m^{-1})(1.00 \times 10^{-9})} = 4.52 \times 10^{-10} </math><br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
'''''How is this topic connected to something that you are interested in?'''''<br />
<br />
This topic is connected to quantum mechanics, a topic that I have been interested in for a while. It amazes me how a particle can tunnel through a higher potential barrier and be observed on the other side when we currently have no means of observing it in the barrier.<br />
<br />
'''''How is it connected to your major?'''''<br />
<br />
I am a physics major...<br />
<br />
'''''Is there an interesting industrial application?'''''<br />
<br />
Although not industrial, quantum tunneling can be attributed to the reason why stars shine. Also, the electron microscope uses quantum tunneling to create a detailed model of nanoscopic objects without coming in contact with them.<br />
<br />
==History==<br />
In his discussion of molecular spectra theory in 1927, Friedrich was the first to utilize the quantum barrier penetration. When he submitted his papers on this theory in 1926, he was supported by household names Niels Bohr and Werner Heisenberg [https://physicstoday.scitation.org/doi/10.1063/1.1510281#:~:text=Friedrich%20Hund%20(1896%E2%80%931997),series%20of%20papers%20in%201927].<br />
111<br />
<br />
==See Also==<br />
[[Heisenberg Uncertainty Principle]]<br />
<br />
[[Wave-Particle Duality]]<br />
<br />
[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
<br />
[[Application of Statistics in Physics]]<br />
<br />
===Further Reading===<br />
*[https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/ Quantum Tunnels Breaking the Speed of Light]<br />
<br />
===External Links===<br />
* [http://abyss.uoregon.edu/~js/glossary/quantum_tunneling.html University of Oregon Quatum Tunneling Page]<br />
<br />
* [https://www.youtube.com/watch?v=cTodS8hkSDg minutephysics What is Quantum Tunneling?]<br />
* [https://www.youtube.com/watch?v=RF7dDt3tVmI Quantum Tunneling Video Simulation]<br />
<br />
==References==<br />
* https://slidetodoc.com/qm-review-and-shm-in-qm-review-and/<br />
* https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.07%3A_Quantum_Tunneling_of_Particles_through_Potential_Barriers<br />
* http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html<br />
* https://phet.colorado.edu/en/simulations/quantum-tunneling<br />
* https://physicstoday.scitation.org/doi/10.1063/1.1510281#:~:text=Friedrich%20Hund%20(1896%E2%80%931997),series%20of%20papers%20in%201927.<br />
<br />
[[Category: Quantum Mechanics]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40710Quantum Theory2022-07-24T19:26:52Z<p>Kaimai: </p>
<hr />
<div>===Claimed by Aellen 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Quantum_Theory&diff=40709Quantum Theory2022-07-24T19:26:23Z<p>Kaimai: </p>
<hr />
<div>===Claimed by kaimai 4/14/2022 (Spring 2022)===<br />
<br />
[[File:BohrModel2.jpg]]<br />
<br />
The Bohr Model of the atom.<br />
<br />
==The Main Idea==<br />
Quantum theory is the accepted modern explanation of the observed behaviors of matter based upon atomic energy and particle interactions. After many notable physicists had hypothesized and disproved various theories to describe the structure of the atom, scientists arrived at the Bohr Model, which currently has the most support from other work and theories from quantum mechanics. After the Rutherford's Gold Foil Experiment, the idea came about that the atom actually exists as many particles held together or near each other by electromagnetic force, which is the attraction or repulsion of charged particles, or the strong force, which holds protons and neutrons together at the nucleus of an atom, and that between these particles there is nothing but empty space. Why these particles stay together in certain configurations and their reactions to incidence with energy or other other particles is explained by quantum physics. The atomic and subatomic characterizations made possible by quantum mechanics differentiate it from classical mechanics. For example, a quantum description of the universe indicates that all objects exhibit a [[Wave-Particle Duality]], meaning all entities express the characteristics of both waves an particles. Additionally, as opposed to classical physics, the elements of momentum, angular momentum, and energy are quantized. In a bound system, they are constrained to discrete values.<br />
<br />
==History==<br />
<br />
The theory and all of its applications, much like any other scientific development of the 20th century, comes from contributions of multiple notable scientists over the course of many years. Initially, Newtonian Laws dominated physics, but the atom was represented by the plum pudding model, which developed after the discovery of the electron and the idea that atom must be made from more particles than previously suspected. None of the leading theories at the time, though, could explain electric discharges or the phenomenon of black lines appearing in the spectra from light passed through various materials. Some scientists were unsure of whether electrons existed as particles or if the electrons themselves were the energy and radiation observed from interactions with atoms. One of the earliest elements that lead to the current model was [[Max Planck]]'s idea that energy could be quantified or defined by smaller units, which he called "quanta". Later, [[Albert Einstein]] applied Planck's work to radiation via what is called the photoelectric effect, where he determined that the results of electron particle interaction with incident radiation, not just energy, depended specifically upon the frequency of the radiation. [[Niels Bohr]] determined his model of atomic structure in 1913; rejecting that idea that electrons orbiting the nucleus eventually radiate energy and fall into the nucleus, he proposed that electrons were held in fixed orbits by electromagnetic forces and that they could shift to other orbits, or other energy levels, by absorption or emission of energy. [[Werner Heisenberg]] also suggested that electrons simply could not possibly be defined by an exact location or momentum by physicists, not without applying some radiation incident to the electron and measuring the disturbance of the system in effect- this idea known as the [[uncertainty principle]]. All of these ideas come together to form our current understanding of quantum physics, which greatly impacts the practice of modern physics.<br />
<br />
==Mathematical Application==<br />
From the development of the quantum theory, we obtain fundamental equations and others which are very useful in introductory physics problems.<br />
<br />
* As Einstein determined, the incident energy that may be absorbed or emitted from electrons (or any particle for this case) depends on the frequency of the radiation:<br />
<br />
<math>{E} = {hν}</math> in units of joules (J)<br />
<br />
where Planck's constant (h) = 64985 Joules/Coloumb and<br />
ν(nu) is the frequency of the radiation, which is also <math>{ν} = {\frac{c}{λ}}</math><br />
<br />
*The radius of an electron's orbit may be determined from:<br />
<br />
<math>{r} = {\frac{Nλ}{2π}}</math> or <math>{r} = {\frac{Nh}{2π|\vec{p}|}}</math><br />
where N is the energy level in which the electron is orbiting and λ is the wavelength<br />
<br />
*From the derivation of the orbit's radius, we can find the angular momentum of the electron:<br />
<br />
<math>{\vec{L}} = {\vec{r}x\vec{p}} = {\frac{Nh}{2π}}</math><br />
<br />
*The centripetal force holding the electron in circular motion is the electromagnetic force produce from the positive charges of the protons in the nucleus and negative charges of the electrons:<br />
<br />
<math> {F_{perpendicular}} = {\frac{mv^2}{r}}</math> <math> {F_{electromagnetic}} = {\frac{1}{4πε_0}\frac{q_e^2}{r^2}}</math><br />
<br />
from this radius of the orbit may also be found with <math>{r} = {\frac{N^2h^2}{ke^24π^2m}}</math> where <math>{k} = {\frac{1}{4πε_0}}</math><br />
<br />
*The total energy of an electron, specifically in the case of the hydrogen atom:<br />
<br />
<math>{E} = {\frac{-13.6}{N^2}}</math> in units of electron volts (eV) where <math>{1eV} = {1.6x10^{-19} J}</math><br />
<br />
*Other energy calculations for an electron orbiting a hydrogen nucleus:<br />
<br />
Potential Energy <math>{U} = {{-}\frac{1}{4πε_0}\frac{q_e^2}{r}}</math> may also be found with <math>{U} = {\frac{-27.2}{N^2}}</math><br />
<br />
Kinetic Energy <math>{K} = {\frac{1}{2}\frac{kq_e^2}{r}}</math><br />
<br />
Total Energy <math>{E_T} = {{U}+{K}} = {{U} + {\frac{-U}{2}}} = {\frac{U}{2}}</math><br />
<br />
Several indices evolve out of the Schrödinger equation solutions for the three-dimensional hydrogen atom. These parameters include the principle quantum number <math>n</math>, where <math>n=1,2,3...</math>, the angular momentum quantum number <math>l</math>, where <math>l=0,1,2,...n-1</math>, and the magnetic quantum number <math>m_l</math>, where <math>m_l=0,±1,±2,...,±l</math>. <br />
<br />
A complete spatial description of electrons within the hydrogen atom is given for the solution to the three-dimensional Schrödinger Equation. For spherical polar coordinates, the solution is separable. The radial function (<math>R</math>), polar function (<math>\Theta</math>), and azimuthal function (<math>\Phi</math>) can be factored as:<br />
<br />
<math> {\Psi(r,\theta,\phi)} = R(r)\Theta(\theta)\Phi(\phi)</math><br />
<br />
The first several solutions to the wavefunction of the hydrogen atom are given below.<br />
<br />
[[File:hydAtom.png]]<br />
<br />
The probability of an electron existing at a given radius from the hydrogen atom can be expressed as:<br />
<br />
<math> P(r)=|\Psi(r,\theta,\phi)|^2dV</math>, which simplifies to<br />
<math> P(r)=r^2|R_n,_l(r)|^2</math><br />
<br />
Integrating over this probability function from one radius to another will provide the probability of an electron appearing in that particular range.<br />
<br />
==Examples==<br />
===Excitation of Hydrogen's Electron===<br />
[[File:Adsporption and emission of photon and energy levels.jpg]]<br />
<br />
Adsorption and Emission of Energy by Electrons.<br />
<br />
If energy is imparted on the orbiting electron of a hydrogen atom, the resulting transfer of energy will raise the energy level of the electron. Since the electron's only applying force prior to the incident energy is the electromagnetic force holding it to the atom, its total energy is negative. Adding energy increases the value of its total energy by an amount equal to that energy adsorbed; furthermore, the only amounts of energy that the electron will take in are those exactly equal to the amount required to completely move it one or more energy levels (meaning it cannot orbit between energy levels, as that event is not stable and the particle will shift immediately to change it). Although electrons are known to move up in energy levels (excited states), it will always release the energy almost immediately after in order to transition back down to a lower energy state (the lowest level known as the ground state E1) where the atom will be more stable and balanced. Applying the full energy that binds the electron to the atom will be a resulting level greater than the extent of the nucleus' attractive force, and the electron will be released from orbit, effectively ionizing the atom.<br />
<br />
[[File:photonEmission.gif]]<br />
<br />
Computational model of photon emission from a hydrogen atom.<br />
<br />
[[File:Energy levels.jpg]]<br />
<br />
Graph illustrating the ground and excited states achieved by electrons with applied radiation. As well, an illustration of how only exact quantities of energy applied have effective results.<br />
<br />
Important to note: If another particle such as an electron collides with the electron of our system, then the amount of energy imparted to our system's electron may any amount required to move up by one or more energy level up to a maximum equal to the total kinetic energy of the colliding electron. If our system's electron gains energy from radiation, such as a photon, then the electron will absorb it completely; therefore, this instance may only occur if the total energy of the photon is equal to the amount required to move up by one or more energy levels.<br />
<br />
[[File:BLSC.png]]<br />
<br />
Multiple elements and their corresponding black line regions of the spectrum at wavelengths which their electrons absorb photons.<br />
<br />
<br />
Applying visible radiation to pure samples allowed scientists to determine which wavelengths of the visible spectrum are absorbed by certain materials and which wavelengths are a reflected. This procedure explained both why we perceive certain colors for specific elements and the black lines of the spectra emitted from samples; the black lines are the locations in the spectra of photons with wavelengths absorbed by the electrons of the atom since they have the exact amount of energy needed to transition to another energy level. All of the other wavelengths are sent away from the atom and eventually taken in by receptors in our eyes.<br />
<br />
[[File:HydAtomProbs.png]]<br />
<br />
Probability densities for the first couple levels of the hydrogen atom.<br />
<br />
The maximally probable location of the election at the lowest level is at the Bohr Radius <math>a_0</math>. As the electron level increases, the average distance of the electron from the center of the atom increases. For an increase from the first to the second electron level, there is also an increase in the number of maxima. The first maxima appears at <math>r=n^2a_0</math>, and occurs for each <math>n</math> where <math>l=n-1</math>. It is also notable that the probability density <math>|\Psi|^2</math> may not equal zero at <math>r=0</math>, but the <math>r^2</math> factor guarantees that <math>P(r)=0</math> at that location.<br />
<br />
==Connectedness==<br />
Quantum physics is considered one of the fundamental concepts of modern physics studies, promoting the establishment of fields of study such as elementary particles, condensed matter, superconductivity, nuclear physics, chemistry, and other applications of radiation to matter. Understanding atomic structure and behavior with radiation is an important concept for studying most of the real world. Especially in fields of physical chemistry and even analytical chemistry are further developed by innovations in theory and thinking. From this understanding, instrumental observations of other parts of the solar system may be analyzed more effectively to determine chemical make-up and behavior on other bodies. Applications of absorbance and transmittance are useful in determining chemical composition, concentration, or effective uses of synthesized compounds.<br />
<gallery><br />
File:Energy analysis.png<br />
File:Product determination.png<br />
File:Further study.gif<br />
File:Reactor.gif<br />
</gallery><br />
<br />
<br />
<br />
<br />
<br />
== See also ==<br />
*[[Atomic Theory]]<br />
*[[Bohr Model]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
<br />
===Further reading===<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. Print.<br />
<br />
===External links===<br />
<br />
*History and Explanation of [http://dwb.unl.edu/Teacher/NSF/C04/C04Links/www.fwkc.com/encyclopedia/low/articles/q/q021000030f.html Quantum Theory]<br />
*Defining [http://whatis.techtarget.com/definition/quantum-theory "What is quantum theory?"]<br />
*[http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html Quantum Processes] Involving Photon Absorption and Emission<br />
*[http://blogs.jccc.edu/astronomy/textbook/unit-two-conceptual-and-observational-tools-of-astronomy/chapter-5-electromagnetic-radiation-and-matter/ Electromagnetic Radiation and Matter]<br />
==References==<br />
<br />
*Chabay R., Sherwood B. Matter and Interactions. 4th ed. Hoboken, NJ: Wiley, 2015. 323-340,445-450. Print.<br />
*"The Fundamental Forces of Nature." Web. Nd. [http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html]<br />
*"Chapter 5: Electromagnetic Radiation and Matter." Johnson County Community College. Web. 2015.<br />
*Krane, Kenneth S. “Chapter 7: The Hydrogen Atom in Wave Mechanics.” Modern Physics, Wiley, Hoboken, NJ, 2020. <br />
<br />
[[Category:Theory]]</div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40708Main Page2022-07-24T19:25:37Z<p>Kaimai: /* Quantum Mechanics */</p>
<hr />
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* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40707Main Page2022-07-24T19:25:30Z<p>Kaimai: /* Quantum Mechanics */</p>
<hr />
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<br />
This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!<br />
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* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
[[Quantum Tunneling through Potential Barriers addition]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40706Main Page2022-07-24T19:25:04Z<p>Kaimai: /* Quantum Mechanics */</p>
<hr />
<div>__NOTOC__<br />
= '''Georgia Tech Student Wiki for Introductory Physics.''' =<br />
<br />
This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!<br />
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== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
*[[Quantum Tunneling through Potential Barriers addition]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40705Main Page2022-07-24T19:24:24Z<p>Kaimai: /* Week 5 */</p>
<hr />
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<br />
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* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
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* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40704Main Page2022-07-24T19:24:04Z<p>Kaimai: /* Week 5 */</p>
<hr />
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* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
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* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
*[[Quantum Tunneling through Potential Barriers 2]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40702Main Page2022-07-24T19:16:33Z<p>Kaimai: </p>
<hr />
<div>__NOTOC__<br />
= '''Georgia Tech Student Wiki for Introductory Physics.''' =<br />
<br />
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== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimaihttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40701Main Page2022-07-24T18:59:17Z<p>Kaimai: /* Quantum Mechanics */</p>
<hr />
<div>__NOTOC__<br />
= '''Georgia Tech Student Wiki for Introductory Physics.''' =<br />
<br />
This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!<br />
<br />
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* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering: Why is the Sky Blue]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
<br />
===main sum===<br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
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<br />
===Week 11===<br />
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====Condensed Matter Physics====<br />
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</div><br />
</div><br />
<br />
===Week 12===<br />
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====The Nucleus====<br />
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*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
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*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
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</div><br />
<br />
===Week 14===<br />
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====Particle Physics====<br />
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*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Kaimai