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Computing Fractional Fourier Transforms

• marmaduke 9y ago
  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#Application https://en.wikipedia.org/wiki/Fractional_Fourier_transform#A... before reading the article. Pretty neat imo.
  • 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 ago
      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.
      • fallingfrog 9y ago
        I 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)