vi CONTENTS 2.2.4 Born Approximation 58 2.2.5 Electron-Atom Scattering 59 2.3 Photo-Electric Effect 2.4 Photon Scattering 61 2.4.1 Amplitudes 7 2.4.2 Cross Section 72 2.4.3 Rayleigh Scattering 2.4.4 Thomson Scattering 7 Problems 3 Symmetries and Conservation Laws 81 3.1 Symmetries and Conservation Laws 3.1.1 Symmetries 88 3.1.2 Conservation Laws 82 3.2 Continuous Symmetry Operators 84 3.2.1 Translations 84 3.2.2 Rotations 3.3 Discrete Symmetry Operators 83 3.4 Degeneracy 8 3.4.1 Example 3.4.2 Isospin 0 Problems 4 Relativistic Quantum Physics 93 4.1 Klein-Gordon Equation 93 4.2 Dirac Equation 4.2.1 Derivation of the Dirac Equation 4.2.2 Probability Density and Current 101 4.3 Solutions of the Dirac Equation,Anti-Particles 104 4.3.1 Solutions of the Dirac Equation 104 4.3.2 Anti-Particles 108 4.4 Spin,Non-Relativistic Limit and Magnetic Moment 111 4.4.1 Orbital Angular Momentum 111 4.4.2 Spin and Total Angular Momentum 112 4.4.3 Helicity 114 4.4.4 Non-Relativistic Limit 116 4.5 The Hydrogen Atom Re-Revisited 120 Problems 124 5 Special Topics 127 5.1 Introduction 127 5.2 Measurements in Quantum Physics 127 5.3 Einstein-Podolsky-Rosen Paradox 129 5.4 Schrodinger's Cat 133vi CONTENTS 2.2.4 Born Approximation 58 2.2.5 Electron-Atom Scattering 59 2.3 Photo-Electric Effect 63 2.4 Photon Scattering 67 2.4.1 Amplitudes 67 2.4.2 Cross Section 72 2.4.3 Rayleigh Scattering 73 2.4.4 Thomson Scattering 75 Problems 78 3 Symmetries and Conservation Laws 81 3.1 Symmetries and Conservation Laws 81 3.1.1 Symmetries 81 3.1.2 Conservation Laws 82 3.2 Continuous Symmetry Operators 84 3.2.1 Translations 84 3.2.2 Rotations 86 3.3 Discrete Symmetry Operators 87 3.4 Degeneracy 89 3.4.1 Example 89 3.4.2 Isospin 90 Problems 91 4 Relativistic Quantum Physics 93 4.1 Klein-Gordon Equation 93 4.2 Dirac Equation 95 4.2.1 Derivation of the Dirac Equation 95 4.2.2 Probability Density and Current 101 4.3 Solutions of the Dirac Equation, Anti-Particles 104 4.3.1 Solutions of the Dirac Equation 104 4.3.2 Anti-Particles 108 4.4 Spin, Non-Relativistic Limit and Magnetic Moment 111 4.4.1 Orbital Angular Momentum 111 4.4.2 Spin and Total Angular Momentum 112 4.4.3 Helicity 114 4.4.4 Non-Relativistic Limit 116 4.5 The Hydrogen Atom Re-Revisited 120 Problems 124 5 Special Topics 127 5.1 Introduction 127 5.2 Measurements in Quantum Physics 127 5.3 Einstein-Podolsky-Rosen Paradox 129 5.4 Schrodinger’s Cat ¨ 133