Q83 · CSIR-NET Chemistry, June 2016

Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Perturbation Theory · Marks: 2 · Difficulty: Medium

The ground state of a certain system with energy $\epsilon_{0}$, is subjected to a perturbation V , yielding a first order correction $\epsilon_{1}$. If $\mathrm{E}_{0}$ is the true ground-state energy of the perturbed system, the inequality that always holds is
(a)$\epsilon_{1} \geq 0$
(b)$\epsilon_{1} \geq \mathrm{E}_{0}$
(c)$\epsilon_{0}+\epsilon_{1} \leq \mathrm{E}_{\mathrm{i}}$
(d)$\epsilon_{0}+\epsilon_{1} \geq \mathrm{E}_{\mathrm{i}}$
Answer
Answer: D ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation
ε₀ + ε₁ is the expectation value of the full H over the unperturbed ground state. By the variation principle it is ≥ E₀ (d).

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