How to derive the Breit equation (Pauli approximation) in position space?

[cddong]

I am reading the H. A. Bethe's book ---quantum mechanics of one and two electron atoms.
In section 39, it is shown how to go from general form to pauli approximation form through momentum space.
who knows how to go directly in position space?

 

[cddong]

ding

 

[Bob S]

Do you mean the Fourier transform approach in Section 39 β on page 179? I have some cryptic notes (in my handwriting) in the margin that I cannot decipher anymore.

Bob S

 

[cddong]

Do you mean the Fourier transform approach in Section 39 β on page 179? I have some cryptic notes (in my handwriting) in the margin that I cannot decipher anymore.

Bob S

Yes, that is what I am reading.

~~~sounds cool~~can you by some means share it?