Statistical Mechanics: A Set Of Lectures

Physics, rather than mathematics, is the focus in this classic graduate lecture note volume on statistical mechanics and the physics of condensed matter. This book provides a concise introduction to basic concepts and a clear presentation of difficult topics, while challenging the student to reflect upon as yet unanswered questions.

Richard P. Feynman was raised in Far Rockaway, New York, and received his Ph.D. from Princeton. He held professorships at both Cornell and the California Institute of Technology. In 1965 he received the Nobel Prize for his work on quantum electrodynamics. He died in 1988.

Editor's Foreword

v

(6)

Acknowledgments

xi

Chapter 1 Introduction to Statistical Mechanics

1

(38)

1.1 The Partition Function

1

(38)

Chapter 2 Density Matrices

39

(33)

2.1 Introduction to Density Matrices

39

(5)

2.2 Additional Properties of the Density Matrix

44

(3)

2.3 Density Matrix in Statistical Mechanics

47

(1)

2.4 Density Matrix for a One-Dimensional Free Particle

48

(1)

2.5 Linear Harmonic Oscillator

49

(4)

2.6 Anharmonic Oscillator

53

(5)

2.7 Wigner's Function

58

(2)

2.8 Symmetrized Density Matrix for N Particles

60

(4)

2.9 Density Submatrix

64

(2)

2.10 Perturbation Expansion of the Density Matrix

66

(1)

2.11 Proof that F is less than or equal to Fo + [H - Ho]o

67

(5)

Chapter 3 Path Integrals

72

(25)

3.1 Path Integral Formation of the Density Matrix

72

(6)

3.2 Calculation of Path Integrals

78

(6)

3.3 Path Integrals by Perturbation Expansion

84

(2)

3.4 Variational Principle for the Path Integral

86

(2)

3.5 An Application of the Variation Theorem

88

(9)

Chapter 4 Classical System of N Particles

97

(30)

4.1 Introduction

97

(3)

4.2 The Second Virial Coefficient

100

(5)

4.3 Mayer Cluster Expansion

105

(6)

4.4 Radial Distribution Function

111

(2)

4.5 Thermodynamic Functions

113

(2)

4.6 The Born-Green Equation for n(2)

115

(2)

4.7 One-Dimensional Gas

117

(3)

4.8 One-Dimensional Gas with Potential of the Form e^(-|x|)

120

(5)

4.9 Brief Discussion of Condensation

125

(2)

Chapter 5 Order-Disorder Theory

127

(24)

5.1 Introduction

127

(3)

5.2 Order-Disorder in One-Dimension

130

(1)

5.3 Approximate Methods for Two Dimensions

131

(5)

5.4 The Onsager Problem

136

(13)

5.5 Miscellaneous Comments

149

(2)

Chapter 6 Creation and Annihilation Operators

151

(47)

6.1 A Simple Mathematical Problem

151

(3)

6.2 The Linear Harmonic Oscillator

154

(2)

6.3 An Anharmonic Oscillator

156

(1)

6.4 Systems of Harmonic Oscillators

157

(2)

6.5 Phonons

159

(3)

6.6 Field Quantization

162

(5)

6.7 Systems of Indistinguishable Particles

167

(9)

6.8 The Hamiltonian and Other Operators

176

(7)

6.9 Ground State for a Fermion System

183

(2)

6.10 Hamiltonian for a Phonon-Electron System

185

(5)

6.11 Photon-Electron Interactions

190

(2)

6.12 Feynman Diagrams

192

(6)

Chapter 7 Spin Waves

198

(23)

7.1 Spin-Spin Interactions

198

(2)

7.2 The Pauli Spin Algebra

200

(2)

7.3 Spin Wave in a Lattice

202

(4)

7.4 Semiclassical Interpretation of Spin Wave

206

(1)

7.5 Two Spin Waves

207

(2)

7.6 Two Spin Waves (Rigorous Treatment)

209

(3)

7.7 Scattering of Two Spin Waves

212

(3)

7.8 Non-Orthogonality

215

(2)

7.9 Operator Method

217

(1)

7.10 Scattering of Spin Waves-Oscillator Analog

218

(3)

Chapter 8 Polaron Problem

221

(21)

8.1 Introduction

221

(4)

8.2 Perturbation Treatment of the Polaron Problem

225

(6)

8.3 Formulation for the Variational Treatment

231

(3)

8.4 The Variational Treatment

234

(7)

8.5 Effective Mass

241

(1)

Chapter 9 Electron Gas in a Metal

242

(23)

9.1 Introduction: The State Function XXX

242

(2)

9.2 Sound Waves

244

(2)

9.3 Calculation of P(R)

246

(2)

9.4 Correlation Energy

248

(1)

9.5 Plasma Oscillation

249

(3)

9.6 Random Phase Approximation

252

(2)

9.7 Variational Approach

254

(1)

9.8 Correlation Energy and Feynman Diagrams

255

(7)

9.9 Higher-Order Perturbation

262

(3)

Chapter 10 Superconductivity

265

(47)

10.1 Experimental Results and Early Theory

265

(4)

10.2 Setting Up the Hamiltonian

269

(4)

10.3 A Helpful Theorem

273

(1)

10.4 Ground State of a Superconductor

274

(3)

10.5 Ground State of a Superconductor (continued)

277

(2)

10.6 Excitations

279

(2)

10.7 Finite Temperatures

281

(4)

10.8 Real Test of Existence of Pair States and Energy Gap

285

(5)

10.9 Superconductor with Current

290

(3)

10.10 Current Versus Field

293

(5)

10.11 Current at a Finite Temperature

298

(5)

10.12 Another Point of View

303

(9)

Chapter 11 Superfluidity

312

(39)

11.1 Introduction: Nature of Transition

312

(7)

11.2 Superfluidity--An Early Approach

319

(2)

11.3 Intuitive Derivation of Wave Functions: Ground State

321

(5)

11.4 Phonons and Rotons

326

(4)

11.5 Rotons

330

(4)

11.6 Critical Velocity

334

(1)

11.7 Irrotational Superfluid Flow

335

(2)

11.8 Rotational of the Superfluid

337

(2)

11.9 A Reasoning Leading to Vortex Lines

339

(4)

11.10 The Lambda Transition in Liquid Helium

343

(8)

Index

351

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Statistical Mechanics: A Set Of Lectures

Summary

Author Biography

Table of Contents

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