NRQM10_3

# NRQM10_3 - Physics 216 Problem Set 3 Spring 2010 DUE...

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Unformatted text preview: Physics 216 Problem Set 3 Spring 2010 DUE: TUESDAY, MAY 11, 2010 MIDTERM ALERT: There is a change of plans for the midterm exam. The midterm exam will be take place from 10–11:45 am on Thursday May 13, 2010 in ISB 231 (our usual classroom). The exam will cover material from the first five topics of the course syllabus and the first three problem sets. During the exam, you may consult Shankar and Baym, your class notes (and any other handwritten notes), and any of the homework solutions and class handouts that are posted on the course website. 1. A system of three unperturbed states consisting of a degenerate pair of states of energy E 1 and a non-degenerate state of energy E 2 is subsequently perturbed, and is represented by the Hamiltonian matrix: E 1 a E 1 b a ∗ b ∗ E 2 , (1) where E 2 > E 1 . The quantities a and b are to be regarded as perturbations that are of the same order but small compared with E 2 − E 1 . (a) Use second order non–degenerate perturbation theory to calculate the perturbed eigenvalues. Is this procedure correct? (b) Use second order degenerate perturbation theory to calculate the perturbed eigen- values. (c) Calculate the eigenvalues exactly and compare with the results of parts (a) and (b). 2. A diatomic molecule behaves like a rigid rotator with a moment of inertia I = Mr 2 , where M is the reduced mass and r is the distance between the atoms. The Hamiltonian can be approximated by: H = vector L 2 2 I . (2) Assume that the molecule consists of two atoms of charge ± e , separated by a distance r ....
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NRQM10_3 - Physics 216 Problem Set 3 Spring 2010 DUE...

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