Statistical mechanics : a survival guide / A.M. Glazer and J.S. Wark.

Format:

Book

Author/Creator:

Glazer, A. M. (Anthony Michael)

Contributor:

Wark, J. S. (Justin S.)

Language:

English

Subjects (All):

Statistical mechanics.

Physical Description:

xiii, 142 pages : illustrations ; 24 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2001.

Summary:

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.

Contents:

1.1 The Role of Statistical Mechanics 1

1.2 Introduction to Coin Tossing 2

1.3 Heads I Win, Tails You Lose 2

1.4 Stirling's Theorem 5

1.5 More Flipping Coins 6

1.6 Distinguishable Particles 8

2 The Statistics of Distinguishable Particles 14

2.1 The Boltzmann Distribution for Distinguishable Particles 14

2.2 Lagrange's Method of Undetermined Multipliers 15

2.3 The Single-Particle Partition Function 21

2.4 Degeneracy 22

2.5 The Partition Function of a System 23

3 Paramagnets and Oscillators 29

3.1 A Spin-1/2 Paramagnet 29

3.2 Paramagnets with Angular Momentum J 34

3.3 The Simple Harmonic Oscillator 36

3.3.1 An Array of 1-D Simple Harmonic Oscillators 36

3.3.2 An Array of 3-D Simple Harmonic Oscillators 38

4 Indistinguishable Particles and Monatomic Ideal Gases 43

4.1 Distinguishable and Indistinguishable States 43

4.2 Identical Gas Particles - Counting the States 45

4.3 The Partition Function of a Monatomic Ideal Gas 51

4.4 Properties of the Monatomic Ideal Gas 52

4.5 More about Adiabatic Expansions 53

4.6 Maxwell-Boltzmann Distribution of Speeds 56

4.7 Gibbs Paradox 56

5 Diatomic Ideal Gases 62

5.1 Other Degrees of Freedom 62

5.2 Rotational Heat Capacities for Diatomic Gases 63

5.3 The Vibrational Partition Function of a Diatomic Gas 65

5.4 Putting it All Together for an Ideal Gas 66

6 Quantum Statistics 69

6.1 Indistinguishable Particles and Quantum Statistics 69

6.2 Bose-Einstein Statistics 71

6.3 Fermi-Dirac Statistics 73

6.4 More on the Quantum Distribution Functions 73

7 Electrons in Metals 77

7.1 Fermi-Dirac Statistics: Electrons in Metals 77

7.2 The Heat Capacity of a Fermi Gas 79

7.3 The Quantum-Classical Transition 82

8 Photons and Phonons 88

8.1 The Photon Gas 88

8.2 Generalized Derivation of the Density of States 89

8.3 Blackbody Radiation 90

8.4 Phonons 92

9 Bose-Einstein Condensation 97

9.2 The Phenomenon of Bose-Einstein Condensation 97

9.3 The Quantum-Classical Transition Revisited 102

10 Ensembles 104

10.2 The Chemical Potential 106

10.3 Ensembles and Probabilities 107

10.4 The Fermi-Dirac and Bose-Einstein Distributions Revisited 110

10.5 Fermi-Dirac Distribution Revisited 110

10.6 Bose-Einstein Distribution Revisited 111

11 The End is in Sight 113

11.1 Phase Space 113

11.2 Equipartition of Energy 115

11.3 Route Map through Statistical Mechanics 116.

Notes:

Includes bibliographical references (page [139]) and index.

ISBN:

0198508158

0198508166

OCLC:

46847156