This is pretty cool. I wrote a program once to simulate the nonrelativistic schrodinger equation, and I noticed that if you put a periodic boundary condition in there (so the right edge wraps around to the left edge) what you appear to get is that the wavefunction runs through a fractional fourier transform to the fourier transform of the original signal, then back again to the original. Has anyone else seen this? Is the schrodinger equation just a fractional fourier transform?