Here is an example of running a simulation in Java code - written by John L. Richardson, Silicon Graphics -
              This JAVA applet integrates the Schrodinger wave equation.
The wave function Psi(x,t) is initially a guassian wave packet moving to the right.

              The probability density p(x,t) = |Psi(x,t)|^2 is shown in black. 

           The real and imaginary parts of Psi(x,t) are shown in blue and green. 

                  The potential energy function v(x) is shown in red. 

Source code by John L. Richardson:
Copyright 1996 Silicon Graphics, Inc.