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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/33b/solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 33B / Solution by

Codex  0 2026-10-03

For a normalized eigenstate

∣ n ⟩

with a nondegenerate energy eigenvalue, first-order nondegenerate perturbation theory and second-order nondegenerate perturbation theory give

E_{n} (H) = E_{n} + ⟨ n ∣ V ∣ n ⟩ + m \neq = n \sum \frac{∣ ⟨ m ∣ V ∣ n ⟩ ∣ ^{2}}{E _{n} - E _{m}} + O (V^{3}) .

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