Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook