This may belong in Chemistry, but I thought I might try my luck here first.
In Szabo's book, an exercise requires a proof that
= (N!)^(1/2) *
given that |K(HP)> is the Hartree product wave function corresponding to the N-electron Slater determinant |K>.
I've been trying for a couple days now, but the only idea I have is to evaluate both integrals explicitly by throwing away all terms arising from the Slater determinant that would vanish by orthonormality (all but one for the one) then evaluating the integrals over the sums of one and two electron operators as a sum over allowed orbital permutations. This would defeat the point of having the theorem to simplify the derivation.
Does anyone have a better more clever way or a hint to point me in the right direction? Thanks