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.