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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 0-486-65401-X 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 ˆ ρ = 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 | ˆ ρ |...
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- Spring '08
- Work, density matrix, Professor Victor Yakovenko