Question Bank MCQ • 1 Mark Section 4: Quantum Mechanics Perturbation theory

QB_PH_115: Perturbation theory

Question Statement

In non-degenerate perturbation theory, the second-order shift to the ground state energy $E_0^{(2)}$ is always:
(A) Negative or zero ($E_0^{(2)} \le 0$)
(B) Strictly positive
(C) Zero identically
(D) Pure imaginary
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $E_0^{(2)} = \sum_{k \ne 0} \frac{|H'_{0k}|^2}{E_0 - E_k} \le 0$ because $E_0 < E_k$.
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