Introduction to Advanced Quantum Physics

Professor Hans Paar has been on the faculty of the University of California San Diego since 1986. He has taught Quantum Physics in all four quarters it is offered at the undergraduate level and has developed and taught the third and fourth quarter of this course (which corresponds to the content of the book) almost each of those 22 years. He has been vice-chair education in UCSD's Physics Department from 1992-1999 and again from 2008-present.Professor Paar is an experimental particle-astrophysicist and has spent nearly 20 years in experimental high energy physics (particle physics by another name) and nearly three years in Cosmology (the Big-Bang and the particle physics of that era). I am an author on 938 publications.

• Preface ixPART 1 Relativistic Quantum Physics 11 Electromagnetic Radiation and Matter 31.1 Hamiltonian and Vector Potential 31.2 Second Quantization 101.2.1 Commutation Relations 101.2.2 Energy 121.2.3 Momentum 171.2.4 Polarization and Spin 191.2.5 Hamiltonian 231.3 Time-Dependent Perturbation Theory 241.4 Spontaneous Emission 281.4.1 First Order Result 281.4.2 Dipole Transition 301.4.3 Higher Multipole Transition 321.5 Blackbody Radiation 361.6 Selection Rules 39Problems 442 Scattering 492.1 Scattering Amplitude and Cross Section 492.2 Born Approximation 522.2.1 Schrödinger Equation 522.2.2 Green’s Function Formalism 522.2.3 Solution of the Schrödinger Equation 552.2.4 Born Approximation 582.2.5 Electron-Atom Scattering 592.3 Photo-Electric Effect 632.4 Photon Scattering 672.4.1 Amplitudes 672.4.2 Cross Section 722.4.3 Rayleigh Scattering 732.4.4 Thomson Scattering 75Problems 783 Symmetries and Conservation Laws 813.1 Symmetries and Conservation Laws 813.1.1 Symmetries 813.1.2 Conservation Laws 823.2 Continuous Symmetry Operators 843.2.1 Translations 843.2.2 Rotations 863.3 Discrete Symmetry Operators 873.4 Degeneracy 893.4.1 Example 893.4.2 Isospin 90Problems 914 Relativistic Quantum Physics 934.1 Klein-Gordon Equation 934.2 Dirac Equation 954.2.1 Derivation of the Dirac Equation 954.2.2 Probability Density and Current 1014.3 Solutions of the Dirac Equation, Anti-Particles 1044.3.1 Solutions of the Dirac Equation 1044.3.2 Anti-Particles 1084.4 Spin, Non-Relativistic Limit and Magnetic Moment 1114.4.1 Orbital Angular Momentum 1114.4.2 Spin and Total Angular Momentum 1124.4.3 Helicity 1144.4.4 Non-Relativistic Limit 1164.5 The Hydrogen Atom Re-Revisited 120Problems 1245 Special Topics 1275.1 Introduction 1275.2 Measurements in Quantum Physics 1275.3 Einstein-Podolsky-Rosen Paradox 1295.4 Schrödinger’s Cat 1335.5 The Watched Pot 1355.6 Hidden Variables and Bell’s Theorem 137Problems 140PART 2 Introduction to Quantum Field Theory 1436 Second Quantization of Spin 1/2 and Spin 1 Fields 1456.1 Second Quantization of Spin 1/2 Fields 1456.1.1 Plane Wave Solutions 1456.1.2 Normalization of Spinors 1466.1.3 Energy 1486.1.4 Momentum 1516.1.5 Creation and Annihilation Operators 1516.2 Second Quantization of Spin 1 Fields 155Problems 1597 Covariant Perturbation Theory and Applications 1617.1 Covariant Perturbation Theory 1617.1.1 Hamiltonian Density 1617.1.2 Interaction Representation 1657.1.3 Covariant Perturbation Theory 1687.2 W and Z Boson Decays 1717.2.1 Amplitude 1717.2.2 Decay Rate 1737.2.3 Summation over Spin 1747.2.4 Integration over Phase Space 1797.2.5 Interpretation 1817.3 Feynman Graphs 1837.4 Second Order Processes and Propagators 1857.4.1 Annihilation and Scattering 1857.4.2 Time-Ordered Product 187Problems 1938 Quantum Electrodynamics 1958.1 Electron-Positron Annihilation 1958.2 Electron-Muon Scattering 201Problems 204Index 207

"The material is intended for undergraduates who are planning to take up the study of elementary particle physics or condensed matter. The problem section given at the end of each chapter is a useful addition for a better understanding of the subject." (Zentralblatt MATH, 2011)