An Introduction to Advanced Quantum Physics presents important concepts from classical mechanics, electricity and magnetism, statistical physics, and quantum physics brought together to discuss the interaction of radiation and matter, selection rules, symmetries and conservation laws, scattering, relativistic quantum mechanics, apparent paradoxes, elementary quantum field theory, electromagnetic and weak interactions, and much more.This book consists of two parts:Part 1 comprises the material suitable for a second course in quantum physics and covers:Electromagnetic Radiation and MatterScatteringSymmetries and Conservation LawsRelativistic Quantum PhysicsSpecial TopicsPart 2 presents elementary quantum field theory and discusses:Second Quantization of Spin 1/2 and Spin 1 FieldsCovariant Perturbation Theory and ApplicationsQuantum ElectrodynamicsEach chapter concludes with problems to challenge the students’ understanding of the material.This text is intended for graduate and ambitious undergraduate students in physics, material sciences, and related disciplines.
Author(s): Hans Paar
Edition: 1
Year: 2010
Language: English
Pages: 224
An Introduction to Advanced Quantum Physics......Page 6
Contents......Page 8
Preface......Page 12
PART 1 Relativistic Quantum Physics......Page 16
1.1 Hamiltonian and Vector Potential......Page 18
1.2.1 Commutation Relations......Page 25
1.2.2 Energy......Page 27
1.2.3 Momentum......Page 32
1.2.4 Polarization and Spin......Page 34
1.2.5 Hamiltonian......Page 38
1.3 Time-Dependent Perturbation Theory......Page 39
1.4.1 First Order Result......Page 43
1.4.2 Dipole Transition......Page 45
1.4.3 Higher Multipole Transition......Page 47
1.5 Blackbody Radiation......Page 51
1.6 Selection Rules......Page 54
Problems......Page 59
2.1 Scattering Amplitude and Cross Section......Page 64
2.2.2 Green’s Function Formalism......Page 67
2.2.3 Solution of the Schr ¨ odinger Equation......Page 70
2.2.4 Born Approximation......Page 73
2.2.5 Electron-Atom Scattering......Page 74
2.3 Photo-Electric Effect......Page 78
2.4.1 Amplitudes......Page 82
2.4.2 Cross Section......Page 87
2.4.3 Rayleigh Scattering......Page 88
2.4.4 Thomson Scattering......Page 90
Problems......Page 93
3.1.1 Symmetries......Page 96
3.1.2 Conservation Laws......Page 97
3.2.1 Translations......Page 99
3.2.2 Rotations......Page 101
3.3 Discrete Symmetry Operators......Page 102
3.4.1 Example......Page 104
3.4.2 Isospin......Page 105
Problems......Page 106
4.1 Klein-Gordon Equation......Page 108
4.2.1 Derivation of the Dirac Equation......Page 110
4.2.2 Probability Density and Current......Page 116
4.3.1 Solutions of the Dirac Equation......Page 119
4.3.2 Anti-Particles......Page 123
4.4.1 Orbital Angular Momentum......Page 126
4.4.2 Spin and Total Angular Momentum......Page 127
4.4.3 Helicity......Page 129
4.4.4 Non-Relativistic Limit......Page 131
4.5 The Hydrogen Atom Re-Revisited......Page 135
Problems......Page 139
5.2 Measurements in Quantum Physics......Page 142
5.3 Einstein-Podolsky-Rosen Paradox......Page 144
5.4 Schr ¨ odinger’s Cat......Page 148
5.5 The Watched Pot......Page 150
5.6 Hidden Variables and Bell’s Theorem......Page 152
Problems......Page 155
PART 2 Introduction to Quantum Field Theory......Page 158
6.1.1 Plane Wave Solutions......Page 160
6.1.2 Normalization of Spinors......Page 161
6.1.3 Energy......Page 163
6.1.5 Creation and Annihilation Operators......Page 166
6.2 Second Quantization of Spin 1 Fields......Page 170
Problems......Page 174
7.1.1 Hamiltonian Density......Page 176
7.1.2 Interaction Representation......Page 180
7.1.3 Covariant Perturbation Theory......Page 183
7.2.1 Amplitude......Page 186
7.2.2 Decay Rate......Page 188
7.2.3 Summation over Spin......Page 189
7.2.4 Integration over Phase Space......Page 194
7.2.5 Interpretation......Page 196
7.3 Feynman Graphs......Page 198
7.4.1 Annihilation and Scattering......Page 200
7.4.2 Time-Ordered Product......Page 202
Problems......Page 208
8.1 Electron-Positron Annihilation......Page 210
8.2 Electron-Muon Scattering......Page 216
Problems......Page 219
Index......Page 222
