Q112 · CSIR NET Chemistry, December 2011
Paper: CSIR NET December 2011 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Perturbation Theory · Marks: 2 · Difficulty: Medium
For non-degenerate perturbation theory for ground state, with $\mathrm{E}_{0}^{(0)}$ as zeroth order energy, $\mathrm{E}_{0}^{(1)}$ as the first-order perturbation correction and $\mathrm{E}_{0}$ as the exact energy, which of the following is true?
(a)$\left(\mathrm{E}_{0}^{(0)}+\mathrm{E}_{0}^{(1)}\right)$ is always equal to $\mathrm{E}_{0}$
(b)$\left(\mathrm{E}_{0}^{(0)}+\mathrm{E}_{0}^{(1)}\right) \leq \mathrm{E}_{0}$
(c)$\left(\mathrm{E}_{0}^{(0)}+\mathrm{E}_{0}^{(1)}\right) \geq \mathrm{E}_{0}$
(d)$\mathrm{E}_{0} \leq\left(\mathrm{E}_{0}^{(1)}+\mathrm{E}_{0}\right)$
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
E₀⁽⁰⁾ + E₀⁽¹⁾ = ⟨ψ⁽⁰⁾|H|ψ⁽⁰⁾⟩, a variational estimate, so it is ≥ the exact E₀ (c).
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