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New here: need help on Fourier transform of wave-function

  1. Aug 3, 2004 #1
    hi, there

    hope someone can help me

    the task is simple, i have to calculate the Fourier tranform of wave-function to get it in momentum space

    the problem is that this is a 4-dimensional space, so the Fourier transform is multi-dimensional

    the only idea i have is that this wave-function has a hyperspherical harmonic as its part, so i guees the book of Avery J. 'Hyperspherical Harmonics: Application to Quantum Theory' can help

    but i can't get it( has anyone seen it? an electronic version, i can't afford to get a printed version(

    also i've read that maybe Fock method can help, but this method is also desribed in the same book(

    cheers, Max
     
  2. jcsd
  3. Aug 4, 2004 #2

    turin

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    Did you try using a kernel of the form:

    e^(i(pμxμ)/h) = ei(ωt-k.x)?

    Is there some reason why you would think this is inappropriate?
     
  4. Aug 6, 2004 #3
    thank you for your feedback

    i do use this kernel to calculate Fourier transform, but the problem is that Schrodinger equation is solved not in ordinal coordinate space but in new 'hyperspherical' coordinates - rho, psi, theta, phi

    so when i start to calculate Fourier transform i have to replace x, y, z, t with their expressions in hyperspherical coordinates so the task becomes more complicated

    and i hope that Avery's book gives the way how to calculate it
     
  5. Aug 6, 2004 #4

    turin

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    Sorry spex.
    I thought you were just asking about the generalization from 1-D to n-D Fourier transform. :redface:

    I don't know how to do what you are trying to do, and I know nothing of "Avery's book."
     
  6. Aug 6, 2004 #5
    ah... damn

    do you know anything on Hankel or Watson transform? or any place where i can find more info about them?
     
  7. Aug 6, 2004 #6

    turin

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    I've never heard of the Watson transform, but I found a brief table of Hankels on the internet. I think it was on that Mathworld website. I'll see if it can find it again and then post the link.

    http://mathworld.wolfram.com/HankelTransform.html
     
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