Wave Packets for Particle in a Box
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.
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 .