For non-degenerate perturbation theory for ground state, with E₀⁽⁰⁾ as zeroth order energy, E₀⁽¹⁾ as the…

Question

For non-degenerate perturbation theory for ground state, with E₀⁽⁰⁾ as zeroth order energy, E₀⁽¹⁾ as the first-order perturbation correction and E₀ as the exact energy, which of the following is true?

Accepted Answer

(c) (E₀⁽⁰⁾+E₀⁽¹⁾) ≥ E₀. Explanation: E₀⁽⁰⁾ + E₀⁽¹⁾ = ⟨ψ⁽⁰⁾|H|ψ⁽⁰⁾⟩, a variational estimate, so it is ≥ the exact E₀ (c).

Answer

(a) (E₀⁽⁰⁾+E₀⁽¹⁾) is always equal to E₀

Answer

(b) (E₀⁽⁰⁾+E₀⁽¹⁾) ≤ E₀

Answer

(d) E₀ ≤ (E₀⁽¹⁾+E₀)

Q112 · CSIR-NET Chemistry, December 2011