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

QB_PH_104: Harmonic oscillator

Question Statement

For the ground state of a 1D quantum oscillator of mass $m$ and frequency $\omega$, $\langle x^2 \rangle = k \frac{\hbar}{m\omega}$. What is $k$?
Correct Answer
0.5, 0.5
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\langle x^2 \rangle = \frac{\hbar}{2m\omega}(2n + 1)$. For $n = 0$: $k = 0.5$.
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