Good evening,
I am looking into the proof of the RS perturbation theory and I do not feel comfortable with the fact that multiplying
(Ei0 - H0|ψi(1)>=(V-Ei1)|i> =(V - <i|V|i>)|i>,
where V = perturbation, i = |Ψi0>, Ei0 is the zeroth-order energy term and H0 is the zeroth-order hamiltonian which eigenfunctions and eigenvalues are considered known, by
<n|,
where <n| comes from the expansion of the first order wavefunction into a linear combination of n atomic orbitals and coefficients,
gives
(Ei0-En0)<n|Ψi1> = <n|V|i>
Does the integral <i|V|i> equal zero? Does the En0 come from the zeroth order hamiltonian? As obvious, I am not comfortable with RSPT yet, that is why I ask on this forum.