Wave Packets for Particle in a Box

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

One of the simplest problems in quantum physics is that of a particle inside a one-dimensional box. This Demonstration shows the time evolution of a packet constructed as a superposition of the first standing waves. The coefficients are such that in the limit the initial wave function would be a square pulse of half-width located at . With finite these two parameters control the position and width of the initial wave packet. You can follow the time evolution of the real and imaginary parts of the wave function, the probability distribution function, and the real part of the standing waves multiplied by their respective coefficients. The circles show the motion of the average position. Units: , and the width of the box is 1.

Contributed by: Andrés Santos (December 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

In the chosen units, the standing wave functions are with .

The (unnormalized) wave packet is , where .

In the limit the initial wave packet tends to a square pulse of half-width located at .



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send