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First-order nondegenerate perturbation theory

For a normalized eigenstate

∣ n ⟩

belonging to a nondegenerate energy eigenvalue,

E_{n}^{(1)} = ⟨ n ∣ V ∣ n ⟩, ∣ n^{(1)} ⟩ = \sum_{m \neq = n} ∣ m ⟩ \frac{⟨ m ∣ V ∣ n ⟩}{E _{n}^{(0)} - E _{m}^{(0)}} .

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