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
. 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.