The angular momentum operator Lz=-iħ(∂)/(∂φ) has eigen functions of the form exp (iAφ). The condition that a… · ABC26PH0157

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

The angular momentum operator $L_z=-i\hbar\dfrac{\partial}{\partial\phi}$ has eigen functions of the form $\exp(iA\phi)$. The condition that a full rotation leaves such an eigen function unchanged is satisfies for all the values of $A$.
(a)$0, \pm\dfrac{1}{3}, \pm\dfrac{2}{3}, \pm1, \pm\dfrac{4}{3}, \ldots$
(b)$0, \pm1, \pm2, \pm3, \pm4, \ldots$
(c)$0, \pm\dfrac{1}{2}, \pm1, \pm\dfrac{3}{2}, \ldots$
(d)$0, \dfrac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2}, \dfrac{7}{2}, \ldots$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
Single-valuedness requires e^(iA·2π) = 1, so A must be an integer: 0, ±1, ±2, … (b).

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