Introductory Quantum Physics And Relativity (Second Edition)

by Jacob Dunningham, Vlatko Vedral

Overview

'The authors have done an exceptional job. It's probably more accurate to describe this text as an introduction to both non-relativistic and relativistic quantum mechanics … This book was a lot of fun to read and digest. I definitely recommend it for instructors, but also for students who have already been exposed to quantum mechanics.'
Contemporary PhysicsThis book is a revised and updated version of Introductory Quantum Physics and Relativity. Based on lectures given as part of the undergraduate degree programme at the University of Leeds, it has been extended in line with recent developments in the field. The book contains all the material required for quantum physics and relativity in the first three years of a traditional physics degree, in addition to more interesting and up-to-date extensions and applications which include quantum field theory, entanglement, and quantum information science.The second edition is unique as an undergraduate textbook as it combines quantum physics and relativity at an introductory level. It expounds the foundations of these two subjects in detail, but also illustrates how they can be combined. It discusses recent applications, but also exposes undergraduates to cutting-edge research topics, such as laser cooling, Bose-Einstein condensation, tunneling microscopes, lasers, nonlocality, and quantum teleportation.

Product Details

ISBN-13:	9789813228641
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/30/2018
Pages:	308
Product dimensions:	6.00(w) x 9.00(h) x 0.75(d)

Table of Contents

Acknowledgements v

1 Introduction 1

2 Old Quantum Theory 9

2.1 Black body radiation 9

2.2 The photoelectric effect 17

2.3 Compton scattering 20

2.4 De Broglie's hypothesis 23

2.5 Bohr's model of the atom 25

2.6 Problems with old quantum theory 29

2.7 Exercises 30

3 Quantum Mechanics 33

3.1 Schrödinger's equation 34

3.2 Bora's postulate 37

3.3 Time-independent Schrödinger equation 38

3.4 Free particle 40

3.5 Observables and operators 40

3.6 The superposition principle 42

3.7 Expectation values 43

3.8 The uncertainty principle 44

3.9 Conceptual foundations of quantum mechanics 45

3.10 Observing the observer 48

3.11 Exercises 53

4 Applications of Quantum Mechanics 55

4.1 Infinite square well 55

4.2 The quantum harmonic oscillator 58

4.3 Tunnelling 60

4.4 Reflection and transmission coefficients 64

4.5 Tunnelling in action 65

4.6 Two level systems 68

4.7 Cold matter 69

4.8 Exercises 73

5 Schrodinger Equation in Three Dimensions 77

5.1 Three-dimensional box 77

5.2 Schrödinger equation in spherical coordinates 79

5.3 Separation of variables 83

5.4 The hydrogen atom 84

5.5 Radial probability densities 87

5.6 Exercises 90

6 Spin and Statistics 91

6.1 Stern-Gerlach experiment 91

6.2 What is spin? 93

6.3 Symmetry of the wave function 95

6.4 Wave function for two identical particles 95

6.5 The Pauli Exclusion Principle 98

6.6 Spin states and spin functions 99

6.7 Bose-Einstein and Fermi-Dirac distributions 100

6.8 Exercises 107

7 Atoms, Molecules and Lasers 109

7.1 Periodic table 109

7.2 Ionisation energies 111

7.3 Energy spectrum 113

7.4 Ionic bonding 114

7.5 Covalent bonding 116

7.6 Van der Waals force 118

7.7 Lasers 119

7.8 The lasing condition 122

7.9 Exercises 125

8 Formal Structure of Quantum Mechanics 127

8.1 States and ensembles 127

8.2 Introduction to Dirac notation 128

8.3 Operators 131

8.4 Measurements 133

8.5 Postulates of quantum mechanics 136

8.6 Position and momentum operators 137

8.7 Position and momentum wave functions 138

8.8 Fourier transforms and the delta function 139

8.9 Position and momentum operators revisited 143

8.10 The Schrodinger equation revisited 145

8.11 The uncertainty principle revisited 146

8.12 Pure and mixed states 148

8.13 Annihilation and creation operators 150

8.14 The Mach-Zehnder interferometer 153

8.15 Perturbation theory 157

8.16 Exercises 162

9 Second Revolution: Relativity 165

9.1 Simultaneity 166

9.2 Lorentz transformations 167

9.3 Length contraction 171

9.4 Time dilation 172

9.5 The twin paradox 175

9.6 Causality 177

9.7 E = Mc² 178

9.8 Relativistic Newton's laws of motion 181

9.9 General relativity 183

9.10 Exercises 185

10 Fine Structure of the Hydrogen Atom 187

10.1 Relativistic correction to the kinetic energy 187

10.2 Addition of angular momenta 190

10.3 Spin-orbit coupling 192

10.4 The Darwin term 197

10.5 Lamb shift 200

10.6 Hyperfine structure 200

10.6.1 Finite mass effects 201

10.6.2 Finite volume effects 202

10.6.3 Nuclear spin 203

10.7 Zeeman shift 206

10.8 Stark shift 210

10.9 Exercises 214

11 Relativistic Quantum Mechanics 217

11.1 Why the need for relativistic quantum mechanics? 217

11.2 The Klein-Gordon equation 218

11.3 Negative probabilities 219

11.4 The Dirac equation 220

11.5 Quantum field theory 222

11.6 Example: Electron transport in a solid 225

11.6.1 Low temperature behaviour 226

11.6.2 High temperature behaviour 228

11.7 Outlook 229

11.8 Exercises 230

12 Quantum Entanglement 231

12.1 What is entanglement? 232

12.2 Bell's inequalities 233

12.3 Quantum teleportation 237

12.4 Why is entanglement necessary? 241

12.5 The non-increase of entanglement under local operations 242

12.6 Entanglement purification 243

12.7 Purification of pure states 247

12.8 Entanglement measures 248

12.9 Thermodynamics of entanglement 252

12.10 Quantum computing 255

12.11 Outlook 257

12.12 Exercises 259

13 Solutions 261

13.1 Chapter 2 261

13.2 Chapter 3 264

13.3 Chapter 4 266

13.4 Chapter 5 271

13.5 Chapter 6 274

13.6 Chapter 7 276

13.7 Chapter 8 279

13.8 Chapter 9 284

13.9 Chapter 10 287

13.10 Chapter 11 290

13.11 Chapter 12 292

Bibliography 295