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Physics Experimentation

Demonstration device of the particle's probability density in one-dimensional infinite square well

YI Qi-shun

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The demonstration device of the particle's probability density in one-dimensional infinite square well is design.Standing wave image of particle's state function is used to demonstrate particle's probability density.The students can intuitively observe the law of particle's probability density at different places in one-dimensional infinite square well.

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The demonstration device of the particle's probability density in one-dimensional infinite square well is design.Standing wave image of particle's state function is used to demonstrate particle's probability density.The students can intuitively observe the law of particle's probability density at different places in one-dimensional infinite square well.
In this article,via numerical method,we have shown the wave function diagrams corresponding to the different analytical solutions of the infinitely deep square potential,and the reason which causes the different phase of the analytic solution has been discussed.The probability density distribution curve is given,through which we found that the probability density distribution of the analytical solutions are identical even though the phase of them are different.This conclusion reflects in one side that a phase factor difference of the wave functions can exist in quantum mechanics.
After briefly reviewing the definitions of classical probability densities for position, P CL ( x ), and for momentum, P CL ( p ), we present several examples of classical mechanical potential systems, mostly variations on such familiar cases as the infinite well and the uniformly accelerated particle for which the classical distributions can be easily derived and visualized. We focus especially on a simple potential which interpolates between the symmetric linear potential, V ( x ) = F | x |, and the infinite well, which can illustrate, in a mathematically straightforward way, how the divergent δ-function classical probability density for momentum for the infinite well can be seen to arise. Such examples can help students understand the quantum mechanical momentum-space wavefunction (and its corresponding probability density) in much the same way that other semiclassical techniques, such as the WKB approximation, can be used to visualize position-space wavefunctions.