First-order nondegenerate perturbation theory
= First-order nondegenerate perturbation theory
For a normalized eigenstate $|n\rangle$ belonging to a <nondegenerate energy eigenvalue>,
$$
E_n^{(1)}=\langle n|V|n\rangle,
\qquad
|n^{(1)}\rangle
=\sum_{m\ne n}|m\rangle
\frac{\langle m|V|n\rangle}{E_n^{(0)}-E_m^{(0)}}.
$$