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Fourier transform with Mathematica (Dirac mean position eigenfunction)

  1. Mar 7, 2005 #1
    Mathematica can't calculate Fourier transform (Dirac mean position eigenfunction)

    Hi, I'm attempting to use Mathematica to calculate a mean-position eigenfunction of the Dirac equation. To do so I need to evaluate Fourier transforms (from p-space to r-space) of wavefunctions dependent on:




    where k is in units of the Compton wavevector.

    Mathematica is unable to evaluate the FT of the above (either Fourier sine transform or normal FT). Can anyone give any suggestions as to how I could evaluate it?

    More specifically, I am making a reverse Foldy-Wouthuysen transformation of a mean-position eigenfunction in p-space, then transforming the result into r-space assuming spherical symmetry. The first component of the r-space eigenfunction is given by the Fourier sine transform of:

    [tex] k\,{\sqrt{1+{\frac1{\sqrt{1+{k^2}}}}}} [/tex]

    Thanks for any help.
    Last edited: Mar 7, 2005
  2. jcsd
  3. Mar 9, 2005 #2
    Hi again, have I posted this in the right forum? If not please suggest where I'm most likely to get an answer!

    Otherwise I would be very grateful if anyone could tell me either how to Fourier transform:

    [tex] k\,{\sqrt{1+{\frac1{\sqrt{1+{k^2}}}}}} [/tex]

    or that it is not possible to do so.
  4. Mar 9, 2005 #3


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    I sure can't, but the function isn't square integrable over k-space in any case.

    Also, it is in very good approximation equal to k.
  5. Mar 9, 2005 #4
    Thanks :).

    Unfortunately it's the difference from k that's important as it is the exact spatial extent of the wavefunction which is of interest (it is a Dirac delta in the untransformed Foldy-Wouthuysen representation since it's a mean position eigenfunction and mean position = r in that representation).
    Last edited: Mar 9, 2005
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