- #1
Jacob
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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.
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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