This textbook is addressed to graduate and post-graduate students in Physics.lt is intended to provide a self-contained introduction to the principles of Quantum Mechanics， based on the analysis of measurement processes of microscopic systems and the introduction of the physical observables as generators of symmetry transformations. After standard training arguments the applications are mainly focused on atomic and nuclear phenomena， as they occur on a quite different space-time scale. Thus， the text flows from the simplest systems， i.e. proton-electron in the Hydrogen atom and proton-neutron in the Deuteron nucleus， to the complex many-body systems， i.e. stable states of atoms and nuclei of the Periodic Table， and finally to infinite many-body systems， including atomic and nuclear fluids. A digression is made on the application to astrophysical compact systems.
目錄：
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
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