(adsbygoogle = window.adsbygoogle || []).push({}); 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:

[tex]

\frac1{{\sqrt{{({1+{k^2}+{\sqrt{1+{k^2}}}})}}}}

[/tex]

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.

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# Fourier transform with Mathematica (Dirac mean position eigenfunction)

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