Q85 · CSIR-NET Chemistry, June 2014

Paper: CSIR-NET June 2014 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Angular Momentum · Marks: 2 · Difficulty: Medium

The angular momentum operator $\mathrm{L}_{\mathrm{z}}=-\mathrm{i} \hbar \frac{\partial}{\partial \phi}$ has eigen functions of the form $\exp (\mathrm{iA} \phi)$. The condition that a full rotation leaves such an eigen function unchanged is satisfies for all the values of A
(a)$0, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm 1, \pm \frac{4}{3}$
(b)$0, \pm 1, \pm 2, \pm 3, \pm 4$
(c)$0, \pm \frac{}{2}, \pm 1, \pm \frac{-}{2}$
(d)$0, \frac{-}{2}, \frac{-}{2}, \frac{1}{2}, \frac{1}{2}$
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
e^(iA·2π) = 1 requires A to be an integer: 0, ±1, ±2, … (b).

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