Questions tagged [perturbation-theory]

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Is the correct zeroth-order wave function $\phi^{(0)}$ an eigenfunction of the perturbation Hamiltonian $H'$?

Consider the perturbation treatment of He $1s2s$ excited state configuration. The quantum mechanical Hamiltonian for the He-atom is: \begin{aligned} \hat{H} = \sum_{i=1}^2 h_i + \frac 1 {r_{1 2}} \\ ...
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Proof for second-order perturbation term of energy

In perturbation theory, if \begin{align}{\hat {H}} &= {\hat {H}^{(0)}} + λ{\hat {H}^{(1)}} \tag{1}\\ {ψ} &= {ψ^{(0)}} + λ{ψ^{(1)}} +λ^2{ψ^{(2)}} + ... \tag{2}\\ {E} &= {E^{(0)}} + λ{E^{...