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Now that we know the functional form for the wavefunction in Hartree-Fock
theory, let's re-examine the Hamiltonian to make it look as simple
as possible. In the process, we will bury some complexity that would
have to be taken care of later (in the evaluation of integrals).
We will define a one-electron operator as follows
and a two-electron operator as
Now we can write the electronic Hamiltonian much more simply, as
Since is just a constant for the fixed set of nuclear coordinates
, we will ignore it for now (it doesn't change the
eigenfunctions, and only shifts the eigenvalues).