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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 don’t have a copy of Bransden yet, the full commutation relations are [ J x ,J y ] = i...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online