pset05

# pset05 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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Vx MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall , 2002 Professor Robert W. Field Problem Set #5 DUE : At the start of Lecture on Friday , October 18. Problems : 1. A. Use the a , a algebra introduced at the end of Lecture #13 to organize the matrix elements of x 3 and x 4 according to selection rules: 3 x n || n + 3 3 x n n + 1 4 x n n + 4 4 x n n + 2 4 n n x B . Use non-degenerate perturbation theory to express the energy levels of () = k x 2 /2 + a x 3 + b x 4 Ev / ) ± ω e x e ( v + 12 / ) 3 ( )/ hc = E 0 / hc + ω e ( v + / ) 2 + ω e y e ( v + where ω e , ω e x e , and ω e y e are traditional vibrational constants. Express E 0 , ω e , ω e x e , and ω e y e in terms of m , k , a , and b . This is an extremely complicated and tedious algebraic nightmare. Maybe you can get your computer to do the algebra. 2. You are going to approach the following potential energy curve using a variety of methods , including the Discrete Variable representation (DVR) and Perturbation Theory: V( x ) = k x 2 /2 – |a| x 3 + |b| x 4 .

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pset05 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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