pset06 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall, 2002 Professor Robert W. Field Problem Set #6 DUE : At the start of Lecture on Friday, October 25. Reading : CTDL pp. 290-307, 1148-1155. [optional, 1169-1199] Problems : 1. You are going to derive the “x–k” relationships given on pages 17-4 and 17-5. You have worked out the relationships between m, k, a , and b in Hp x x x =+ + + 22 3 4 2 1 2 / mkab and Y 00 , ω e , ω e x e in Eh cY n xn ne e e /( / ) ( / ) + + 00 2 12 ωω , for a single-oscillator (diatomic) molecule. Now you are going to consider 3N–6 anharmonically coupled, anharmonic oscillators in an N-atom polyatomic molecule. The only thing that is different is that there are many more terms in H (1) and the E n () 2 terms involve short summations over several combinations of oscillators. In all of your derivations ignore the h m ω / factor that makes q dimensionless.
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Chemistry 5.73 Page 2 Problem Set #6 A. x ii appears in the energy level expression as Ex n nn n i i i N 12 3 6 2 =+ () L / . The first term in the equation for x ii on page 17-4 comes from one of the two strictly diagonal matrix elements of H (1) .
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pset06 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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