Heisenberg Uncertainty Principle: Difference between revisions
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'''NOTE:''' <math>{\hbar = \frac{{h}}{2\pi}}</math> where <math>{h}</math> is Planck's constant. | '''NOTE:''' <math>{\hbar = \frac{{h}}{2\pi}}</math> where <math>{h}</math> is Planck's constant. | ||
This principle can also be extended to a relationship between energy and time, where: | |||
<math>{\Delta E \Delta t >= \frac{{\hbar}}{2}}</math> | |||
<math>{\Delta E \Delta t}</math> ~ <math>{\hbar}</math> | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 10:18, 18 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.
This principle can also be extended to a relationship between energy and time, where:
[math]\displaystyle{ {\Delta E \Delta t \gt = \frac{{\hbar}}{2}} }[/math]
[math]\displaystyle{ {\Delta E \Delta t} }[/math] ~ [math]\displaystyle{ {\hbar} }[/math]
A Computational Model
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Examples
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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.
See also
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References
Krane, K. S. (2020). Modern physics. Wiley.