Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the… · ABC26PH0180

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Perturbation Theory · Exam: CSIR NET 2020 · Marks: 2 · Difficulty: Medium

Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the perturbation being $H'=\mu E \cos \phi E$, where $\mu$ is the dipole moment. The energy levels correct upto first order are Options:
(a)$\frac{m_{l}^{2} \mathrm{h}^{2}}{2}-\frac{\mu E}{\pi}$
(b)$\frac{m_{l}^{2} \mathrm{h}^{2}}{2 I}-\frac{\mu E}{2 \pi}$
(c)$\frac{m_{l}^{2} \mathrm{h}^{2}}{2 I}+\frac{\mu E}{2 \pi}$
(d)$\frac{m_{l}^{2} \mathrm{h}^{2}}{2 I}$
Answer
Answer: D ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation
E⁽¹⁾ = ⟨m|μE cos φ|m⟩ = (μE/2π)∫₀^{2π} cos φ dφ = 0, so to first order the levels stay at m_l²ħ²/2I.

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