量子力学:从原子到原子核

本书以量子力学与经典力学的对应为线索，通过时空对称性与能量、动量和角动量守恒之间的紧密联系这一普适关系探讨量子力学与经典力学的对应关系，并实现该书内容的组织逻辑。通过与经典哈密顿量力学作类比，由时空变换的生成元引入力学量，帮助同学更深入地理解经典概念到量子概念的过渡。书中介绍了量子力学的基本原理及其在物理各个分支领域的应用，如光学、原子物理、固体物理、原子核物理和核天体物理，试图通过具体应用举例来引导学生更深刻地理解量子力学原理。该书的一个特色是针对核物理专业的学生做了针对性的介绍，讲述了量子力学的相对论拓展，引入了处理量子多体系统的方法和近似，包括从有限多体系统到均匀无限大系统，并以原子核和中子星为例进行讲解，给出计算实例便于读者理解。该书还设计了练习题，并可提供解答提示和相关数值程序。

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
……