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P19.11 Show that the selection rule for the two-dimensional rotor in the dipole approximation is Am₁ = ±1. Use A+em and A'+eim₂ for the initial and final states of the rotor and ucos as the dipole moment element.

P19.11 Show that the selection rule for the two-dimensional rotor in the dipole approximation is Am₁ = ±1. Use A+em and A'+eim₂ for the initial and final states of the rotor and ucos as the dipole moment element.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Problem P19.11** Show that the selection rule for the two-dimensional rotor in the dipole approximation is \( \Delta m_l = \pm 1 \). Use \( A_{+\phi} e^{i m_1 \phi} \) and \( A'_{+\phi} e^{i m_2 \phi} \) for the initial and final states of the rotor, and \( \mu \cos \phi \) as the dipole moment element.
Transcribed Image Text:**Problem P19.11** Show that the selection rule for the two-dimensional rotor in the dipole approximation is \( \Delta m_l = \pm 1 \). Use \( A_{+\phi} e^{i m_1 \phi} \) and \( A'_{+\phi} e^{i m_2 \phi} \) for the initial and final states of the rotor, and \( \mu \cos \phi \) as the dipole moment element.
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