p137bp1 - Physics 137B, Fall 2007 Quantum Mechanics II...

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Unformatted text preview: Physics 137B, Fall 2007 Quantum Mechanics II Problem set 1 : review, esp. angular momentum and spin Assigned Friday, 30 August. Due in box Friday, 7 September, 5 pm. Assume every Friday that there is a new problem set unless I say otherwise in class. Starting next week, problem sets will assume you have a copy of Bransden. They should be downloaded from the course webpage http://socrates.berkeley.edu/jemoore/p137b/p137b.html. 1. Show that the commutator [ J 2 ,J z ] = 0, where J 2 = J x 2 + J y 2 + J z 2 . Do not use the orbital angular momentum expression L = r p . Instead use the general angular momentum commutation relations, which can be written compactly as [ J i ,J j ] = i h ijk J k (1) where the Levi-Civita antisymmetric symbol is formally defined in Bransden problem 6.4. This symbol gives just the same pattern of signs as in a cross product: ( r p ) i = ijk r i p j . If you dont have a copy of Bransden yet, the full commutation relations are [ J x ,J y ] = i...
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