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homework7 - Homework#7 PHYS 603 Spring 2007 Deadline...

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Homework #7 — PHYS 603 — Spring 2007 Deadline: Tuesday, May 8, 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. 9 Quantum Statistics of Independent Particles 1. Problem 9.1, Applying the three statistics to a two-level system. Derive answers analytically. Do not substitute numbers. 2. Problem 9.2, No Bose-Einstein condensation for free particle in D = 1 , 2 . 3. Problem 9.3, Adiabatic relation holds for any statistics. You may use virial theorem (2.39). 4. Problem 9.4, Entropy for Fermi statistics. 5. Problem 9.5, Entropy for any statistics. 6. Problem 9.6, Entropy for Bose statistics. Also read Problem 9.7 and its solution for your information. You don’t need to submit it, because solution is written in the book. 7. UMD qualiﬁer problem, January 2005: 1D Fermi gas. Use results of Sec. 14-4 for this Problem. Consider a one-dimensional (1D) noninteracting free electron gas moving along the x axis with a number density of n electrons per unit length. Assume the electronic wavefunctions to be the usual plane wave momentum eigenstates with the electron energy being quadratic in momentum: ε = p 2 / 2 m . Give the answers to the questions below in terms of Planck’s constant ¯ h , the electron mass m , Boltzmann’s constant k B , the 1D electron density

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homework7 - Homework#7 PHYS 603 Spring 2007 Deadline...

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