# matrix elements of the electronic molecular Hamiltonian between a hartree product and a Slater determinant

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

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Something is missing in your equation. Can you complete it? –  suresh Jul 18 at 0:13
Is that Szabo and Ostlund's book Modern Quantum Mechanics? If so, what exercise are you referring to i.e. what number? –  John Rennie Jul 18 at 9:32