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Unformatted text preview: Homework #3 PHYS 603 Spring 2007 Deadline: Thursday, April 5, 2007, in class Professor Victor Yakovenko Office: 2115 Physics Web page: http://www2.physics.umd.edu/yakovenk/teaching/ Textbook: Gregory H. Wannier, Statistical Physics Dover 1987 reprint of the 1966 edition, ISBN 048665401X Do not forget to write your name and the homework number! Each problem is worth 10 points. Ch. 3 Statistical Counting in Mechanics 1. Problem 3.2, Phase space per quantum state for an oscillator. 2. Problem 3.4, Phase space per quantum state for a particle in a box. 3. Properties of the density matrix. (a) Using Eq. (3.16), show that Tr = 1. (b) Suppose Eq. (3.16) is written in the energy representation, where the indices i and j represent energy eigenstates. Then, the coefficients in Eq. (3.14) have the following time dependence: a j e iE j t/ h . Show that, after averaging over a long time, the density matrix (3.16) becomes diagonal in the energy representation h i  ...
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