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573pset10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall , 2002 Professor Robert W. Field Problem Set #10 DUE : At the start of Lecture on Friday , December 6. Reading : Golding Handout Problems : 1. A. Use the method of M L , M S boxes to determine the L,S terms that belong to the d 2 , d 2 p, and nd 2 n d electronic configurations. Use (and explain) shortcuts to deal with the d 2 , d 2 p, and nd 2 n d configurations. B. What is the total degeneracy of the d 3 configuration? Use this result to direct your guesswork in determining the L–S terms that belong to d 3 by using your result for nd 2 n d and eliminating inappropriate L–S terms. C. Use the ladders plus orthogonality method to derive the linear combination of Slater determinants that corresponds to the d 2 3 P M L = 1, M S = 0 state. D. Use 3 – j coefficients to construct L = 1, M L = 1, S = 1, M S = 0 from 1 1 2 2 2 1 2 2 1 1 2 1 1 2 1 2 1 = = ( ) = = = = − ( ) , , / , , , / , m s m m m s m m S s s combinations of spin-orbitals. The relevant coupled
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