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MathGroup Archive 2005

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Mathematica can't calculate Fourier transform (Dirac mean position eigenfunction)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54979] Mathematica can't calculate Fourier transform (Dirac mean position eigenfunction)
  • From: "Jacob" <jacob.linacre at gmail.com>
  • Date: Tue, 8 Mar 2005 05:04:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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 k-space to r-space) of wavefunctions dependent
on:

( (1 + k^2 + (1 + k^2)^(1/2) )^(-1/2)

where k is in units of the Compton wavevector.

Cell expression:

Cell[BoxData[
    FractionBox["1",
      SqrtBox[
        RowBox[{"1", "+",
          SuperscriptBox["k", "2"], "+",
          SqrtBox[
            RowBox[{"1", "+",
              SuperscriptBox["k", "2"]}]]}]]]], "Output"]


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:

k ( 1 + (1 + k^2)^(-1/2) )^(1/2)

Cell[BoxData[
    RowBox[{"k", " ",
      SqrtBox[
        RowBox[{"1", "+",
          FractionBox["1",
            SqrtBox[
              RowBox[{"1", "+",
                SuperscriptBox["k", "2"]}]]]}]]}]], "Output"]


Thanks for any help.


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