Statistical Mechanics A Survival Guide

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ISBN: 9780198508168 | 0198508166
Cover: Paperback
Copyright: 9/27/2001

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The present book is a teaching text designed to introduce the fundamentals of the subject of statistical mechanics at a level suitable for students who meet the subject for the first time. The treatment given is designed to give the student a feeling for the topic of statistical mechanics without being held back by the need to understand complex mathematics. The text is concise and concentrates on the understanding of fundamental aspects. Numerous questions with worked solutions are given throughout.

Back to Basics	p. 1
The Role of Statistical Mechanics	p. 1
Introduction to Coin Tossing	p. 2
Heads I Win, Tails You Lose	p. 2
Stirling's Theorem	p. 5
More Flipping Coins	p. 6
Distinguishable Particles	p. 8
Summary	p. 11
Problems	p. 12
The Statistics of Distinguishable Particles	p. 14
The Boltzmann Distribution for Distinguishable Particles	p. 14
Lagrange's Method of Undetermined Multipliers	p. 15
The Single-Particle Partition Function	p. 21
Degeneracy	p. 22
The Partition Function of a System	p. 23
Summary	p. 25
Problems	p. 26
Paramagnets and Oscillators	p. 29
A Spin-1/2 Paramagnet	p. 29
Paramagnets with Angular Momentum J	p. 34
The Simple Harmonic Oscillator	p. 36
An Array of 1-D Simple Harmonic Oscillators	p. 36
An Array of 3-D Simple Harmonic Oscillators	p. 38
Summary	p. 40
Problems	p. 41
Indistinguishable Particles and Monatomic Ideal Gases	p. 43
Distinguishable and Indistinguishable States	p. 43
Identical Gas Particles - Counting the States	p. 45
The Partition Function of a Monatomic Ideal Gas	p. 51
Properties of the Monatomic Ideal Gas	p. 52
More about Adiabatic Expansions	p. 53
Maxwell-Boltzmann Distribution of Speeds	p. 56
Gibbs Paradox	p. 56
Summary	p. 59
Problems	p. 61
Diatomic Ideal Gases	p. 62
Other Degrees of Freedom	p. 62
Rotational Heat Capacities for Diatomic Gases	p. 63
The Vibrational Partition Function of a Diatomic Gas	p. 65
Putting it All Together for an Ideal Gas	p. 66
Summary	p. 67
Problems	p. 68
Quantum Statistics	p. 69
Indistinguishable Particles and Quantum Statistics	p. 69
Bose-Einstein Statistics	p. 71
Fermi-Dirac Statistics	p. 73
More on the Quantum Distribution Functions	p. 73
Summary	p. 76
Problems	p. 76
Electrons in Metals	p. 77
Fermi-Dirac Statistics: Electrons in Metals	p. 77
The Heat Capacity of a Fermi Gas	p. 79
The Quantum-Classical Transition	p. 82
Summary	p. 85
Problems	p. 86
Photons and Phonons	p. 88
The Photon Gas	p. 88
Generalized Derivation of the Density of States	p. 89
Blackbody Radiation	p. 90
Phonons	p. 92
Summary	p. 93
Problems	p. 94
Bose-Einstein Condensation	p. 97
Introduction	p. 97
The Phenomenon of Bose-Einstein Condensation	p. 97
The Quantum-Classical Transition Revisited	p. 102
Summary	p. 102
Problems	p. 103
Ensembles	p. 104
Introduction	p. 104
The Chemical Potential	p. 106
Ensembles and Probabilities	p. 107
The Fermi-Dirac and Bose-Einstein Distributions Revisited	p. 110
Fermi-Dirac Distribution Revisited	p. 110
Bose-Einstein Distribution Revisited	p. 111
Summary	p. 111
Problems	p. 112
The End is in Sight	p. 113
Phase Space	p. 113
Equipartition of Energy	p. 115
Route Map through Statistical Mechanics	p. 116
Summary	p. 118
Problems	p. 118
Worked Answers to Problems	p. 119
Chapter 1	p. 119
Chapter 2	p. 120
Chapter 3	p. 122
Chapter 4	p. 124
Chapter 5	p. 125
Chapter 6	p. 126
Chapter 7	p. 126
Chapter 8	p. 128
Chapter 9	p. 132
Chapter 10	p. 133
Chapter 11	p. 134
Useful Integrals	p. 137
Physical Constants	p. 138
Bibliography	p. 139
Index	p. 140
Table of Contents provided by Syndetics. All Rights Reserved.

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Statistical Mechanics A Survival Guide

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