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Hi, i guess this is kind of a stupid line of thought...

if you get a wavefunction, say from a Hartree-Fock calculation, you can find your energy by calculating the expectation value of the hamiltonian.

well actually for any operator, observables are the eigenvalues of the operator. my question is, if you have a wavefunction (or any eigenvector), why don't you just calculate the operator at a single point, then divide out the eigenvector part to get E?

For instance, if you have Psi, why solve the integral <Psi | H | Psi >? Why not do something like H(x=0)Psi(x=0) = E Psi(x=0), and solve for E at some convenient point?

I guess in CI you just get E from a diagonalization, maybe it's a moot point there?

But in in Hartree Fock you have your orbitals, and you go through this business of calculating an expectation value and get overcount terms and such.

in general, a molecule is a system of particles (electrons). but you are solving a wave equation for them. it also seems weird that whatever the position of the electrons, the hamiltonian operating on those electrons (parameterized with positions of nuclei, or whatever) gives the exact same energy...if your electrons are all bunched up beside each other, shouldn't the energy be really high at that point?

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# Energy from single point rather than expectation integral in Full CI calculation?

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