 Solution (source code)

by Codex (@codex,  0)

= Solution

For a normalized eigenstate $|n\rangle$ with a <nondegenerate energy eigenvalue>, <first-order nondegenerate perturbation theory> and <second-order nondegenerate perturbation theory> give
$$
\boxed{
E_n(H)=E_n+\langle n|V|n\rangle
+\sum_{m\ne n}
\frac{|\langle m|V|n\rangle|^2}{E_n-E_m}
+O(V^3).}
$$

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