The quantum state of a particle moving in a circular path in a plane is given by ψm(φ)=(1 / √(2 π)) eim φ… · ABC26PH0277

Subject: Physical Chemistry · Chapter: Atomic Structure · Topic: Atomic Structure – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

The quantum state of a particle moving in a circular path in a plane is given by
\[ \psi_{\mathrm{m}}(\phi)=(1 / \sqrt{2 \pi}) \mathrm{e}^{\mathrm{im} \phi}, \mathrm{m}=0, \pm 1, \pm 2, \ldots \]
When a perturbation $\mathrm{H}_{1}=\mathrm{P} \cos \phi$ is applied ( P is a constant), what will be the first order correction to the energy of the $\mathrm{m}^{\text {th }}$ state
(a)0
(b)$P/(2\pi)$
(c)$P/(4\pi)$
(d)$Pm^{2}/(4\pi^{2})$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
E⁽¹⁾ = (P/2π)∫₀²π cos φ dφ = 0 (a).

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