Heisenberg Uncertainty Principle: Difference between revisions

Revision as of 14:24, 17 April 2022

Claimed by Bernardo Perez 4/17/22

Short Description of Topic

Heisenberg Uncertainty Principle

The Heisenberg uncertainty principle is a concept that describes uncertainty relationships between a particle's different properties, those being position and momentum, as well as energy and time. The biggest takeaway from this concept is that there is always some measure of uncertainty in at least one of any given particle's properties.

A Mathematical Model

The total uncertainty between a particle's position and momentum is given as [math]\displaystyle{ {\Delta p \Delta x} }[/math]. The minimum uncertainty a particle can have is [math]\displaystyle{ {\frac{{\hbar}}{2}} }[/math]. Therefore, we can establish the relationship of:

[math]\displaystyle{ {\Delta p \Delta x \gt = \frac{{\hbar}}{2}} }[/math]

Oftentimes, it is also good enough to simply approximate their general relationship as:

[math]\displaystyle{ {\Delta p \Delta x} }[/math] ~ [math]\displaystyle{ {\hbar} }[/math]

NOTE: [math]\displaystyle{ {\hbar = \frac{{h}}{2\pi}} }[/math] where [math]\displaystyle{ {h} }[/math] is Planck's constant.

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

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Connectedness

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History

The development of the Heisenberg uncertainty principle is largely accredited to Werner Heisenberg.

Single-slit Diffraction Experiments

Heisenberg uncertainty relationships were first physically demonstrated through single-slit diffraction experiments. The experiment is conducted by launching beam of electrons through a narrow slit. Initially, the electrons have zero momentum in the x-direction. After passing through the slit, information about an electron's x position is acquired, resulting in an increased uncertainty in the particle's x momentum. Making the slit narrower therefore increases the uncertainty of the particle's x momentum while decreasing the uncertainty of its x position, while making the slit wider has the opposite effect. This effectively demonstrates the relationship between the uncertainty of a particle's position and momentum.

@@ Line 8: / Line 8: @@
 ===A Mathematical Model===
+The total uncertainty between a particle's position and momentum is given as <math>{\Delta p \Delta x}</math>. The minimum uncertainty a particle can have is <math>{\frac{{\hbar}}{2}}</math>. Therefore, we can establish the relationship of:
+<math>{\Delta p \Delta x >= \frac{{\hbar}}{2}}</math>
+Oftentimes, it is also good enough to simply approximate their general relationship as:
+<math>{\Delta p \Delta x}</math> ~ <math>{\hbar}</math>
+'''NOTE:''' <math>{\hbar = \frac{{h}}{2\pi}}</math> where <math>{h}</math> is Planck's constant.
 What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

Heisenberg Uncertainty Principle: Difference between revisions

Revision as of 14:24, 17 April 2022

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