In the final form of the two-electron potential matrix <l1,l2,L,M|
1/r_12 |l1',l2',L',M'>, I think there is no factor (2L+1).
This factor will be eliminated in constructing the six-J symbols.
I think the first two "=" are correct, but the third one
(the last "=" sign) is not. After summing up over M, there cannot be
any M left in the equation. So I think we are missing a summation over
M in the last equation there.
That way the 2L+1 factor disappears from the final formula for the two electron integral, as it should.
Reported by Liguang G. Jiao.
http://theoretical-physics.net/dev/src/quantum/hf.html#two-particle
In the final form of the two-electron potential matrix <l1,l2,L,M| 1/r_12 |l1',l2',L',M'>, I think there is no factor (2L+1). This factor will be eliminated in constructing the six-J symbols.
I think the first two "=" are correct, but the third one (the last "=" sign) is not. After summing up over M, there cannot be any M left in the equation. So I think we are missing a summation over M in the last equation there.
That way the 2L+1 factor disappears from the final formula for the two electron integral, as it should.