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E-grāmata: Quantum Theory and Statistical Thermodynamics: Principles and Worked Examples

Peter Hertel

Formāts: EPUB+DRM
Sērija : Graduate Texts in Physics
Izdošanas datums: 16-Aug-2017
Izdevniecība: Springer International Publishing AG
Valoda: eng
ISBN-13: 9783319585956

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Formāts: EPUB+DRM
Sērija : Graduate Texts in Physics
Izdošanas datums: 16-Aug-2017
Izdevniecība: Springer International Publishing AG
Valoda: eng
ISBN-13: 9783319585956

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This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles necessarily rather abstract are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well.

The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers.

Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix.

The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced

optics, and other modern fields.

Recenzijas

The textbook is intended for students of general physics, chemistry, molecular biology, material science and even for philosophical minded readers. The many worked examples are presented at various levels of abstraction. (Vladimir Dzhunushaliev, zbMATH 1379.81009, 2018)

1 Basics

(30)

1.1 Introduction

(4)

1.1.1 The Quantum of Light

(1)

1.1.2 Electron Diffraction

(1)

1.1.3 Heisenberg Uncertainty Principle

(1)

1.1.4 Does God Play Dice?

(1)

1.1.5 Summary

(1)

1.2 Classical Framework

(6)

1.2.1 Phase Space

(1)

1.2.2 Observables

(1)

1.2.3 Dynamics

(2)

1.2.4 States

(1)

1.2.5 Properties of Poisson Brackets

(1)

1.2.6 Canonical Relations

(1)

1.2.7 Pure and Mixed States

(1)

1.2.8 Summary

(1)

1.3 Quantum Framework

(10)

1.3.1 q-Numbers

(1)

1.3.2 Hilbert Space

(1)

1.3.3 Linear Operators

(2)

1.3.4 Projectors

(1)

1.3.5 Normal Linear Operators

(2)

1.3.6 Trace of an Operator

(1)

1.3.7 Expectation Values

(1)

1.3.8 Summary

(1)

1.4 Time and Space

(9)

1.4.1 Measurement and Experiment

(1)

1.4.2 Time Translation

(1)

1.4.3 Space Translation

(1)

1.4.4 Location

(1)

1.4.5 Rotation

(1)

1.4.6 Orbital Angular Momentum and Spin

(1)

1.4.7 Schrodinger Picture

(1)

1.4.8 Summary

(2)

2 Simple Examples

(34)

2.1 Ammonia Molecule

(7)

2.1.1 Hilbert Space and Energy Observable

(1)

2.1.2 Ammonia Molecule in an External Electric Field

(1)

2.1.3 Dipole Moment Expectation Value

(1)

2.1.4 Ammonium Maser

(1)

2.1.5 Summary

(1)

2.2 Quasi-Particles

(8)

2.2.1 Hilbert Spaces Cn and l2

(2)

2.2.2 Hopping Model

(1)

2.2.3 Wave Packets

(1)

2.2.4 Group Velocity and Effective Mass

(1)

2.2.5 Scattering at Defects

(2)

2.2.6 Trapping by Defects

(1)

2.2.7 Summary

(1)

2.3 Neutron Scattering on Molecules

(7)

2.3.1 Feynman's Approach

(1)

2.3.2 Spherical and Plain Waves

(1)

2.3.3 Neutron Scattering on a Diatomic Molecule

(1)

2.3.4 Cross Section

(1)

2.3.5 Orientation Averaged Cross Section

(2)

2.3.6 Neutron Diffraction

(1)

2.3.7 Summary

(1)

2.4 Free Particles

(7)

2.4.1 Square Integrable Functions

(1)

2.4.2 Location

(1)

2.4.3 Linear Momentum

(2)

2.4.4 Wave Packets

(1)

2.4.5 Motion of a Free Particle

(1)

2.4.6 Spreading of a Free Particle

(1)

2.4.7 Summary

(1)

2.5 Small Oscillations

(5)

2.5.1 The Hamitonian

(1)

2.5.2 Ladder Operators

(1)

2.5.3 Eigenstate Wave Functions

(1)

2.5.4 Summary

(1)

3 Atoms and Molecules

(46)

3.1 Radial Schrodinger Equation

(6)

3.1.1 Spherical Coordinates

(1)

3.1.2 The Laplacian

(1)

3.1.3 Spherical Harmonics

(2)

3.1.4 Spherical Symmetric Potential

(1)

3.1.5 Behavior at Origin and Infinity

(1)

3.1.6 Alternative Form

(1)

3.1.7 Summary

(1)

3.2 Hydrogen Atom

(10)

3.2.1 Atomic Units

(2)

3.2.2 Non-relativistic Hydrogen Atom

(1)

3.2.3 Orbitals

(2)

3.2.4 Relativistic Hydrogen Atom

(3)

3.2.5 Classical Hydrogen Atom

(1)

3.2.6 Summary

(1)

3.3 Helium Atom

(7)

3.3.1 Wave Functions

(2)

3.3.2 Minimal Ground State Energy

(2)

3.3.3 Sample Calculation

(2)

3.3.4 The Negative Hydrogen Ion

(1)

3.3.5 Summary

(1)

3.4 Hydrogen Molecule

(7)

3.4.1 Wave Functions and Hamiltonian

(2)

3.4.2 Born--Oppenheimer Approximation

(1)

3.4.3 The Molecular Potential

(2)

3.4.4 Molecular Vibrations

(2)

3.4.5 Molecular Rotations

(1)

3.4.6 Summary

(1)

3.5 More on Approximations

(6)

3.5.1 The Minimax Theorem

(1)

3.5.2 Remarks

(2)

3.5.3 Stationary Perturbations

100

(1)

3.5.4 Coping with Degeneracies

101

(1)

3.5.5 Summary

101

(1)

3.6 Stark and Zeeman Effect

102

(9)

3.6.1 Multipoles

102

(3)

3.6.2 Electric Dipole Moment

105

(1)

3.6.3 Stark Effect

106

(2)

3.6.4 Magnetic Dipole Moment

108

(1)

3.6.5 Zeeman Effect

109

(1)

3.6.6 Summary

110

(1)

4 Decay and Scattering

111

(26)

4.1 Forced Transitions

112

(7)

4.1.1 Time Dependent External Field

112

(3)

4.1.2 Detailed Balance

115

(1)

4.1.3 Incoherent Radiation

115

(4)

4.1.4 Summary

119

(1)

4.2 Spontaneous Transitions

119

(4)

4.2.1 Einstein's Argument

119

(2)

4.2.2 Lifetime of an Excited State

121

(1)

4.2.3 Comment on Einstein's Reasoning

121

(1)

4.2.4 Classical Limit

122

(1)

4.2.5 Summary

123

(1)

4.3 Scattering Amplitude

123

(6)

4.3.1 Cross Section

124

(1)

4.3.2 Scattering Amplitude

125

(1)

4.3.3 Center of Mass and Laboratory Frame

126

(2)

4.3.4 Relativistic Description

128

(1)

4.3.5 Summary

129

(1)

4.4 Coulomb Scattering

129

(8)

4.4.1 Scattering Schrodinger Equation

130

(1)

4.4.2 Bom Approximation

131

(1)

4.4.3 Scattering of Point Charges

132

(1)

4.4.4 Electron-Hydrogen Atom Scattering

133

(1)

4.4.5 Form Factor and Structure

134

(2)

4.4.6 Summary

136

(1)

5 Thermal Equilibrium

137

(88)

5.1 Entropy and the Gibbs State

138

(12)

5.1.1 Observables and States

139

(2)

5.1.2 First Main Law

141

(1)

5.1.3 Entropy

142

(3)

5.1.4 Second Main Law

145

(1)

5.1.5 The Gibbs State

146

(1)

5.1.6 Free Energy and Temperature

147

(1)

5.1.7 Chemical Potentials

148

(1)

5.1.8 Minimal Free Energy

149

(1)

5.1.9 Summary

150

(1)

5.2 Thermodynamics

150

(10)

5.2.1 Reversible and Irreversible Processes

151

(1)

5.2.2 Free Energy as Thermodynamic Potential

152

(1)

5.2.3 More Thermodynamic Potentials

153

(1)

5.2.4 Heat Capacity and Compressibility

154

(2)

5.2.5 Chemical Potential

156

(2)

5.2.6 Chemical Reactions

158

(1)

5.2.7 Particle Number as an External Parameter

158

(2)

5.2.8 Summary

160

(1)

5.3 Continuum Physics

160

(13)

5.3.1 Material Points

161

(1)

5.3.2 Balance Equations

162

(1)

5.3.3 Particles, Mass and Electric Charge

163

(2)

5.3.4 Conduction and Covariance

165

(2)

5.3.5 Momentum, Energy, and the First Main Law

167

(3)

5.3.6 Entropy and the Second Main Law

170

(2)

5.3.7 Summary

172

(1)

5.4 Second Quantization

173

(7)

5.4.1 Number Operators

173

(2)

5.4.2 Plane Waves

175

(1)

5.4.3 Local Quantum Field

175

(1)

5.4.4 Fermions

176

(2)

5.4.5 Some Observables

178

(1)

5.4.6 Time

179

(1)

5.4.7 Summary

180

(1)

5.5 Gases

180

(18)

5.5.1 Fermi Gas

181

(3)

5.5.2 Bose Gas

184

(2)

5.5.3 Black-Body Radiation

186

(1)

5.5.4 Boltzmann Gas

187

(3)

5.5.5 Rotating and Vibrating Molecules

190

(2)

5.5.6 Cluster Expansion

192

(2)

5.5.7 Joule-Thomson Effect

194

(2)

5.5.8 Summary

196

(2)

5.6 Crystal Lattice Vibrations

198

(9)

5.6.1 Phenomenological Description

198

(2)

5.6.2 Phonons

200

(7)

5.6.3 Summary

207

(1)

5.7 Electronic Band Structure

207

(7)

5.7.1 Hopping Model

208

(1)

5.7.2 Fermi-Energy

209

(2)

5.7.3 The Cold Solid

211

(1)

5.7.4 Metals, Dielectrics and Semiconductors

212

(1)

5.7.5 Summary

213

(1)

5.8 External Fields

214

(11)

5.8.1 Matter and Electromagnetic Fields

214

(3)

5.8.2 Alignment of Electric Dipoles

217

(1)

5.8.3 Alignment of Magnetic Dipoles

218

(2)

5.8.4 Heisenberg Ferromagnet

220

(3)

5.8.5 Summary

223

(2)

6 Fluctuations and Dissipation

225

(36)

6.1 Fluctuations

226

(11)

6.1.1 An Example

227

(1)

6.1.2 Density Fluctuations

228

(2)

6.1.3 Correlations and Khinchin's Theorem

230

(2)

6.1.4 Thermal Noise of a Resistor

232

(1)

6.1.5 Langevin Equation

232

(2)

6.1.6 Nyquist Formula

234

(2)

6.1.7 Remarks

236

(1)

6.1.8 Summary

236

(1)

6.2 Brownian Motion

237

(7)

6.2.1 Einstein's Explanation

237

(4)

6.2.2 The Diffusion Coefficient

241

(1)

6.2.3 Langevin's Approach

242

(2)

6.2.4 Summary

244

(1)

6.3 Linear Response Theory

244

(9)

6.3.1 Perturbations

245

(5)

6.3.2 Dispersion Relations

250

(2)

6.3.3 Summary

252

(1)

6.4 Dissipation

253

(8)

6.4.1 Wiener--Khinchin Theorem

253

(1)

6.4.2 Kubo--Martin--Schwinger Formula

254

(1)

6.4.3 Callen--Welton Theorem

255

(2)

6.4.4 Interaction with an Electromagnetic Field

257

(2)

6.4.5 Summary

259

(2)

7 Mathematical Aspects

261

(60)

7.1 Topological Spaces

261

(7)

7.1.1 Abstract Topological Space

262

(1)

7.1.2 Metric Space

263

(1)

7.1.3 Linear Space with Norm

264

(1)

7.1.4 Linear Space with Scalar Product

265

(1)

7.1.5 Convergent Sequences

265

(1)

7.1.6 Continuity

266

(1)

7.1.7 Cauchy Sequences and Completeness

267

(1)

7.2 The Lebesgue Integral

268

(4)

7.2.1 Measure Spaces

268

(1)

7.2.2 Measurable Functions

269

(1)

7.2.3 The Lebesgue Integral

270

(1)

7.2.4 Function Spaces

271

(1)

7.3 On Probabilities

272

(5)

7.3.1 Probability Spaces

272

(1)

7.3.2 Random Variables

273

(3)

7.3.3 Law of Large Numbers and Central Limit Theorem

276

(1)

7.4 Generalized Functions

277

(6)

7.4.1 Test Functions

278

(1)

7.4.2 Distributions

278

(1)

7.4.3 Derivatives

279

(1)

7.4.4 Fourier Transforms

280

(3)

7.5 Linear Spaces

283

(3)

7.5.1 Scalars

284

(1)

7.5.2 Vectors

284

(1)

7.5.3 Linear Subspaces

284

(1)

7.5.4 Dimension

285

(1)

7.5.5 Linear Mappings

285

(1)

7.5.6 Ring of Linear Operators

285

(1)

7.6 Hilbert Spaces

286

(3)

7.6.1 Operator Norm

288

(1)

7.6.2 Adjoint Operator

288

(1)

7.7 Projection Operators

289

(2)

7.7.1 Projectors

289

(2)

7.7.2 Decomposition of Unity

291

(1)

7.8 Normal Operators

291

(5)

7.8.1 Spectra] Decomposition

291

(2)

7.8.2 Unitary Operators

293

(1)

7.8.3 Self-Adjoint Operators

294

(1)

7.8.4 Positive Operators

295

(1)

7.8.5 Probability Operators

295

(1)

7.9 Operator Functions

296

(2)

7.9.1 Power Series

296

(1)

7.9.2 Normal Operator

297

(1)

7.9.3 Comparison

297

(1)

7.9.4 Example

297

(1)

7.10 Translations

298

(4)

7.10.1 Periodic Boundary Conditions

299

(1)

7.10.2 Domain of Definition

299

(1)

7.10.3 Selfadjointness

300

(1)

7.10.4 Spectral Decomposition

301

(1)

7.11 Fourier Transform

302

(4)

7.11.1 Fourier Series

302

(1)

7.11.2 Fourier Expansion

303

(1)

7.11.3 Fourier Integral

303

(1)

7.11.4 Convolution Theorem

304

(2)

7.12 Position and Momentum

306

(3)

7.12.1 Test Functions

306

(1)

7.12.2 Canonical Commutation Rules

307

(1)

7.12.3 Uncertainty Relation

308

(1)

7.12.4 Quasi-Eigenfunctions

308

(1)

7.13 Ladder Operators

309

(5)

7.13.1 Raising and Lowering Operators

310

(1)

7.13.2 Ground State and Excited States

310

(1)

7.13.3 Harmonic Oscillator

311

(1)

7.13.4 Quantum Fields

312

(2)

7.14 Transformation Groups

314

(7)

7.14.1 Group

314

(1)

7.14.2 Finite Groups

314

(1)

7.14.3 Topological Groups

315

(3)

7.14.4 Angular Momentum

318

(3)

Glossary

321

(40)

Index

361

Prof. Dr. Peter Hertel studied physics, mathematics and philosophy at the universities of Hamburg (Germany), London (Imperial College, UK) and Vienna (Austria) where he received his Ph.D. His scientific career led him to Heidelberg (Germany), CERN (Geneva, Switzerland), Vienna and Osnabrück (Germany) where he was appointed full professor. Although retired by now, he continues lecturing at the Applied Physics School of Nankai University (Tianjin, China). His research interests were elementary particles, statistical thermodynamics, theoretical optics and computational physics. For more than 40 years he has taught practically all subjects of theoretical physics and mathematics at different levels

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E-grāmata: Quantum Theory and Statistical Thermodynamics: Principles and Worked Examples

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