A numerical solution of the time-dependent Schroedinger equation in one dimension for a particle confined to a region  0 ≤ x ≤ L with a potential step at x = 3L/4.
Reference: S. E. Koonin, Computational Physics, Addison-Wesley Publishing Company Inc, (1986).

Excel2.xlsm is a macro enabled Excel spreadsheet that you can download.  It demonstrates a method for solving the time-dependent Schroedinger equation in one dimension.  The evolution of the wave packet is represented graphically.  (The initial wave packet is Gaussian.)  You are encouraged to modify the program, change the a user interface or translate it to another programming language.
Wavepacket2.m is a MATLAB script implementing the same method.

For an explanation of the program see Program 1.