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Second-order nondegenerate perturbation theory

For a normalized nondegenerate eigenstate

∣ n ⟩

,

E_{n}^{(2)} = \sum_{m \neq = n} \frac{∣ ⟨ m ∣ V ∣ n ⟩ ∣ ^{2}}{E _{n}^{(0)} - E _{m}^{(0)}} .

For a ground state, every denominator is negative, so the correction is nonpositive.

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