量子力学:从原子到原子核:from atoms to nuclei

Contents Chapter 1 Space-Time Symmetries and Classical Observables 1 1.1 Hamilton's Equations 1 1.2 Space-Time Symmetries and Conservation of Dynamical Variables 2 1.3 Canonical Transformations and Space-Time Symmetries 4 1.4 Notes and References 8 1.5 Problems 8 Chapter 2 Superposition Principle 10 2.1 An Historic Experiment 10 2.2 Wave-like Behaviour of Particles 11 2.3 Particle-like Behaviour of Waves 14 2.4 The Stern-Gerlach Experiment 16 2.5 Notes and References 17 2.6 Problems 18 Chapter 3 States and Dynamical Variables 19 3.1 States of a Quantum System as Vectors of Hilbert Space 20 3.2 Observables as Operators in Hilbert Space 22 3.3 General Properties of Quantum Observables 23 3.4 Unitary Transformations 24 3.5 Notes and References 25 3.6 Problems 25 Chapter 4 Space Translations and Momentum 26 4.1 Wave Function and Position Operator 26 4.2 Space Translations 28 4.3 Momentum as a Generator of Infinitesimal Translations 29 4.4 Free Particle in a Box 30 4.5 Heisenberg Uncertainty Relations 33 4.6 Notes and References 37 4.7 Problems 37 Chapter 5 Elementary Phenomena 38 5.1 Double-Slit Interference 38 5.2 Diffraction Grating 40 5.3 Double-Layer Reflection 40 5.4 Scattering of Identical Particles 41 5.5 Notes and References 43 5.6 Problems 44 Chapter 6 Space Rotations and Angular Momentum 45 6.1 Space Rotations 45 6.2 Orbital Angular Momentum as Generator of Infinitesimal Rotations 46 6.3 Properties of the Angular Momentum 47 6.4 Orbital Angular Momentum in Polar Coordinates 50 6.5 Reflection of Axes and Parity 52 6.6 Spin 53 6.7 The Rigid Rotor 55 6.8 Complement to Sec.6.1: Infinitesimal Space Rotations 56 6.9 Notes and References 57 6.10 Problems 58 Chapter 7 Time Translations and Hamiltonian 59 7.1 Time Evolution Operator 59 7.2 Equations of Motion 61 7.3 Stationary Schr.dinger Equation 63 7.3.1 Schr.dinger Equation for Potential Wells 63 7.3.2 Attractive Well: V0 < 0 65 7.3.3 Repulsive Well: V0 > 0 67 7.3.4 Potential Barrier: 0 < E < V0 68 7.3.5 Potential Barrier: E > V0 > 0 69 7.4 Problems 70 Chapter 8 Harmonic Oscillations 71 8.1 Quantum Harmonic Oscillator 72 8.1.1 Eigenfunctions of the Harmonic Oscillator 73 8.2 Vibrations of a Crystal Lattice 74 8.2.1 Small Oscillations in Classical Approach 74 8.2.2 Small Oscillations in Quantum Approach 79 8.3 Three-Dimensional Harmonic Oscillator 79 8.4 Notes and References 81 8.5 Problems 81 Chapter 9 Approximations to Schr.dinger's Equation 83 9.1 Perturbation Theory 83 9.1.1 Non-Degenerate Case 83 9.1.2 Degenerate Case 84 9.2 Variational Approach 86 9.3 Perturbation vs. Variational Approximations for 4He 87 9.3.1 Perturbation Method 88 9.3.2 Variational Estimate 89 9.4 Problems 90 Chapter 10 Time-Dependent Equations of Motion 92 10.1 Heisenberg Representation 92 10.2 Two-Level Quantum System 93 10.2.1 Unperturbed Hamiltonian 93 10.2.2 Perturbation Potential 94 10.2.3 Time-Dependent Hamiltonian 95 10.3 Relationship between Symmetries and Conservation Theorems 96 10.4 Classical Limit: Ehrenfest Theorem 97 10.5 Particle Detection in Scattering Processes 99 10.6 Problems 102 Chapter 11 Time-Dependent Perturbation Theory 104 11.1 Interaction Representation 104 11.2 Electron Transitions in Atoms 106 11.3 Dipole Approximation 108 11.4 Slow vs. Fast Processes 109 11.5 Complement to Sec.11.2: Interaction of Charged Particles with the Electromagnetic Field 112 11.6 Notes and References 113 11.7 Problems 113 Chapter 12 Two-Body Problem: Bound States 115 12.1 Central Potential 115 12.2 Hydrogen Atom 118 12.3 Isospin 121 12.4 Ground State of the Deuteron 124 12.5 Complement to Sec.12.4: Tensor Interaction 126 12.6 Notes and References 127 12.7 Problems 127 Chapter 13 Two-Body Problem: Scattering States 129 13.1 Lippmann-Schwinger Equation 129 13.2 Asymptotic Form of the Continuum States 130 13.3 Solving the Lippmann-Schwinger Equation 133 13.4 Elastic Scattering Cross Section 134 13.4.1 Born Approximation for the Elastic Scattering Cross Section 135 13.4.2 Nuclear and Coulomb Potential 136 13.4.3 Electron Scattering and Nuclear Density 138 13.5 Partial-Wave Analysis 140 13.6 Low-Energy Scattering and Bound States 141 13.7 Nuclear Interaction from Nucleon-Nucleon Scattering 147 13.8 Notes and References 150 13.9 Problems 151 Chapter 14 Many-Body Systems 152 14.1 Systems of Identical Particles 152 14.2 The Hartree-Fock Approximation 155 14.3 Atomic Structure 161 14.4 Nuclear Structure 166 14.4.1 The Nuclear Shell Model 166 14.4.2 Liquid Drop Model and Nuclear Matter 170 14.4.3 Microscopic Approaches 174 14.5 Complement to Sec.14.2: Second Quantization 177 14.6 Complement to Sec.14.4.1: Iso