Question Bank MCQ • 2 Marks Section 4: Quantum Mechanics Harmonic oscillator

QB_PH_114: Harmonic oscillator

Question Statement

For a 1D harmonic oscillator, the dipole transition matrix element $\langle m | x | n \rangle$ is non-zero only if:
(A) \Delta n = m - n = \pm 1
(B) \Delta n = 0
(C) \Delta n = \pm 2
(D) \text{Any integer}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $x = \sqrt{\frac{\hbar}{2m\omega}}(a + a^\dagger)$ connects states with $\Delta n = \pm 1$.
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