●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 ition 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
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本書以量子力學與經典力學的對應為線索，通過時空對稱性與能量、動量和角動量守恆之間的緊密聯繫這一普適關繫探討量子力學與經典力學的對應關繫，並實現該書內容的組織邏輯。通過與經典哈密頓量力學作類比，由時空變換引入力學量，幫助同學更深入地理解經典概念到量子概念的過渡。書中介紹了量子力學的基本原理及其在物理各個分支領域的應用，如光學、原子物理、固體物理、原子核物理和核天體物理，試圖通過具體應用舉例來引導學生更深刻地理解量子力學原理。該書的一個特色是針對核物理專業的學生做了針對性的介紹，講述了量子力學的相對論拓展，引入了處理量子多體繫統的方法和近似，包括從有限多體繫統到均勻無限大繫統，並以原子核和中子星為例進行講解，給出計算實例便於讀者理解。該書還設計了練習題，並可提供解答提示和相關數值程序。