
Computing Fractional Fourier Transforms - panic
http://algassert.com/post/1710
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marmaduke
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...](https://en.wikipedia.org/wiki/Fractional_Fourier_transform#Application)

before reading the article. Pretty neat imo.

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fallingfrog
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?

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tfgg
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.

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

