4 ms·
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 i
by fallingfrog 9y ago
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?
- tfgg 9y agoCould you elaborate why you think it looks like a fractional FT? If you solve Schrödinger's equation with periodic boundary conditions on the potential what you get are Bloch functions, which are the product of a phasor and a periodic function.
- fallingfrog 9y agoI thought so because the evolution of the waveform looked exactly like this: https://upload.wikimedia.org/wikipedia/commons/e/e3/FracFT_Rec_by_stevencys.jpg https://upload.wikimedia.org/wikipedia/commons/e/e3/FracFT_R... (from the wikipedia page on a fractional fourier transform)