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UMD PHYS 402 - Homework #4

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Phys 402 Spring 2009 Homework 4 Due Friday, February 27, 2009 @ 9 AM EXAM #1, covering all material up to and including this HW assignment will be held on Wednesday March 4, 2009 from 9:00 AM to 10:50 AM in Phys 1201. 1. Griffiths, 2nd Edition, Problem 6.16 Commutators of L, S and J! Start with [Lx, Ly] = iħLz, [Sx, Sy] = iħSz, etc. 2. Griffiths, 2nd Edition, Problem 6.17 Add the relativistic and spin-orbit first-order energy corrections to get the fine structure formula. Consider the cases j = l ± ½ separately. 3. Griffiths, 2nd Edition, Problem 6.29 Perturbation of H-atom GS energy due to finite size of the nucleus. Be careful to write down the perturbing Hamiltonian H’ correctly (it has 2 terms)! 4. Griffiths, 2nd Edition, Problem 4.35 Combine spin angular momenta for 2 and 3 spin-1/2 particles 5. Griffiths, 2nd Edition, Problem 4.36 Coupled vs. un-coupled representations of two spins. Use of CG tables. Extra Credit #6 Griffiths, 2nd Edition, Problem 6.32 Feynman-Hellmann theorem for expectation values of operators.Physics 402 Spring 2009 Prof. Anlage Discussion Worksheet for February 25, 2009 1. The Clebsch-Gordan coefficients allow us to go back and forth between the “coupled” and “un-coupled” wavefunctions for multiple-spin systems. Consider two spin-1/2 particles described by kets 121m and 221m. Using Table 4.8 on page 188 of Griffiths, write down the triplet and singlet states of the coupled representation in terms of the uncoupled single-particle kets.2. Consider again two spin-1/2 particles. Using Table 4.8 on page 188 of Griffiths, write down the uncoupled single-particle wavefunctions in terms of the coupled kets sms


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