By Sidney B. Cahn, Gerald D. Mahan, Boris E. Nadgorny, Max Dresden

In order to equip hopeful graduate scholars with the information essential to go the qualifying exam, the authors have assembled and solved general and unique difficulties from significant American universities – Boston college, collage of Chicago, collage of Colorado at Boulder, Columbia, collage of Maryland, college of Michigan, Michigan kingdom, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, collage of Tennessee at Knoxville, and the collage of Wisconsin at Madison – and Moscow Institute of Physics and know-how. quite a lot of fabric is roofed and comparisons are made among related difficulties of other faculties to supply the coed with adequate info to suppose cozy and assured on the examination. *Guide to Physics Problems* is released in volumes: this e-book, *Part 2,* covers Thermodynamics, Statistical Mechanics and Quantum Mechanics; *Part 1,* covers Mechanics, Relativity and Electrodynamics.

Praise for *A advisor to Physics difficulties: half 2: Thermodynamics, Statistical Physics, and Quantum Mechanics:*

"… *A advisor to Physics difficulties, half 2* not just serves a major functionality, yet is a excitement to learn. through choosing difficulties from assorted universities or even varied medical cultures, the authors have successfully kept away from a one-sided method of physics. all of the difficulties are solid, a few are very attention-grabbing, a few certainly interesting, a number of are loopy; yet them all stimulate the reader to consider physics, now not only to coach you to cross an examination. i myself bought huge excitement in operating the issues, and that i could bet that anybody who desires to be a qualified physicist could event related amusement. … This booklet could be a very good aid to scholars and professors, in addition to a resource of enjoyment and enjoyment." (From Foreword by way of Max Dresden)

"An very good source for graduate scholars in physics and, one expects, additionally for his or her teachers." (Daniel Kleppner, Lester Wolfe Professor of Physics Emeritus, MIT)

"A great choice of difficulties … Thought-provoking, exciting, and simply undeniable enjoyable to solve." (Giovanni Vignale, division of Physics and Astronomy, collage of Missouri at Columbia)

"Interesting certainly and relaxing. the issues are inventive and their recommendations very informative. i might definitely suggest it to all graduate scholars and physicists mostly … really invaluable for academics who want to take into consideration difficulties to provide of their course." (Joel Lebowitz, Rutgers University)

"A very completely assembled, attention-grabbing set of difficulties that covers the most important parts of physics addressed via Ph.D. qualifying tests. … Will turn out most valuable to either college and scholars. certainly, I plan to exploit this fabric as a resource of examples and illustrations that might be labored into my lectures." (Douglas generators, college of California at Irvine)

**Read Online or Download A Guide to Physics Problems Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics PDF**

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**Extra resources for A Guide to Physics Problems Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics**

**Example text**

40 Gas in Harmonic Well (Boston) A classical system of N distinguishable noninteracting particles of mass is placed in a three-dimensional harmonic well: a) Find the partition function and the Helmholtz free energy. b) Regarding V as an external parameter, find the thermodynamic force conjugate to this parameter, exerted by the system; find the equation of state and compare it to that of a gas in a container with rigid walls. c) Find the entropy, internal energy, and total heat capacity at constant volume.

A) Find the Fermi energy. b) Show that the total energy is given by c) Qualitatively discuss the behavior of the heat capacity of this system at low temperatures. 66 Nonrelativistic Electron Gas (Stony Brook, Wisconsin-Madison, Michigan State) a) Derive the relation between pressure and volume of a free nonrelativistic electron gas at zero temperature. b) The formula obtained in (a) is approximately correct for sufficiently low temperatures (the so-called strongly degenerate gas). Discuss the applicability of this formula to common metals.

42 Equipartition Theorem (Columbia, Boston) a) For a classical system with Hamiltonian PROBLEMS 22 at a temperature show that b) Using the above, derive the law of Dulong and Petit for the heat capacity of a harmonic crystal. c) For a more general Hamiltonian, prove the generalized equipartition theorem: where You will need to use the fact that U is infinite at d) Consider a system of a large number of classical particles and assume a general dependence of the energy of each particle on the generalized coordinate or momentum component given by where Show that, in thermal equilibrium, the generalized equipartition theorem holds: What conditions should be satisfied for tition theorem?