Solution
= Solution
For a nondegenerate level, <time-independent perturbation theory> gives
$$
\boxed{E_n(\lambda)=E_n+\lambda\langle n|\Delta H|n\rangle
+\lambda^2\sum_{m\ne n}
\frac{|\langle m|\Delta H|n\rangle|^2}{E_n-E_m}+O(\lambda^3)}.
$$
= Solution
For a nondegenerate level, <time-independent perturbation theory> gives
$$
\boxed{E_n(\lambda)=E_n+\lambda\langle n|\Delta H|n\rangle
+\lambda^2\sum_{m\ne n}
\frac{|\langle m|\Delta H|n\rangle|^2}{E_n-E_m}+O(\lambda^3)}.
$$