Computing Fractional Fourier Transforms

algassert.com

51 pointspanic4 comments

It might be helpful to see how this can be interpreted as a rotation in the time-frequency domain,

https://en.wikipedia.org/wiki/Fractional_Fourier_transform#A...

before reading the article. Pretty neat imo.

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?

Could 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.

I thought so because the evolution of the waveform looked exactly like this: https://upload.wikimedia.org/wikipedia/commons/e/e3/FracFT_R... (from the wikipedia page on a fractional fourier transform)

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