ps4 - Physics 212 Spring 2010 Problem Set 4 1. C-TDL Ch. X...

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Unformatted text preview: Physics 212 Spring 2010 Problem Set 4 1. C-TDL Ch. X problem 1 2. C-TDL Ch. X problem 3 3. Show, using a plane wave as your original eigenstate, that the momentum operator generates a translation in space. Prove that a unitary operator U may be written in terms of a Hermitian operator G , where U = exp( iG ), where is arbitrary. 4. Adding l = 1 with s = 1 / 2: Use raising and lowering operators as well as orthogonality to express the combined basis states in terms of the individual basis states | l = 1 ,m l ,s = 1 / 2 ,m s i . 5. Shankar 12.5.7 6. Sakurai Ch. 3 Problem 8 (Sakurai is on reserve in the library if you want to see the problems in their original form. If that is inconvenient, they are reproduced here): Consider a sequence of Euler rotations represented by D 1 / 2 ( ,, ) = exp (- i 3 2 ) exp (- i 2 2 ) exp (- i 3 2 ) . [The (1 / 2) superscript on D means that we are in a spin 1/2 system, so the matrices are the Pauli matrices.] Because of the group properties of rotations, we expect that this sequence of operations is equivalent to a...
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This document was uploaded on 10/20/2011.

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