Which of the following statements on ground state perturbation theory, involving the zeroth order energy… · ABC26PH1308
Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Perturbation Theory · Exam: CSIR NET JUNE 2016 · Marks: 2 · Difficulty: Medium
Which of the following statements on ground state perturbation theory, involving the zeroth order energy $\mathrm{E}_{0}^{(0)}$, first order energy correction $\mathrm{E}_{0}^{(1)}$ and second order energy correction $\mathrm{E}_{0}^{(2)}$, is false?
(a)$\mathrm{E}_{0}^{(1)}$ is the average value of perturbation operator with respect to the ground state of the zeroth order Hamiltonian.
(b)$\mathrm{E}_{0}^{(1)}$ is necessarily negative.
(c)$\mathrm{E}_{0}^{(2)}$ is necessarily negative.
(d)$\mathrm{E}_{0}^{(0)} \mathrm{E}_{0}^{(1)}$ is an upper bound to the exact ground state energy.
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
E₀⁽¹⁾ = ⟨ψ₀⁽⁰⁾|V|ψ₀⁽⁰⁾⟩ can have either sign; the second-order correction to the ground state is always negative, and E⁽⁰⁾ + E⁽¹⁾ is a variational upper bound. So (b) is false.