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Quantum Mechanics: from Atom to Nuclei(量子力学：从原子到原子核)


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Quantum Mechanics: from Atom to Nuclei(量子力学：从原子到原子核)
  • 书号：9787030720344
    作者：（意）翁贝托·隆巴尔多（U. Lombardo）等
  • 外文书名：
  • 装帧：平装
    开本：窄32
  • 页数：278
    字数：400000
    语种：en
  • 出版社：科学出版社
    出版时间：2022-06-01
  • 所属分类：
  • 定价： ￥158.00元
    售价： ￥124.82元
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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.
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目录

  • 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: Isotropic 3-Dimensional Harmonic Oscillator 179
    14.7 Notes and References 182
    14.8 Problems 182
    Chapter 15 The Dirac Equation 184
    15.1 The Klein-Gordon Equation 184
    15.2 Dirac’s Equation 186
    15.2.1 Diagonalization of the Hamiltonian 187
    15.2.2 The Spin Variable 188
    15.3 Covariant Form of the Dirac Equation 189
    15.4 The Spin-Orbit Interaction 191
    15.5 Complement to Sec.15.4: Semi-Classical Hamiltonian 193
    15.6 Notes and References 194
    15.7 Problems 194
    Chapter 16 Homogeneous Many-Body Systems 195
    16.1 Gibbs Statistical Approach 195
    16.2 Time Average and Statistical Average 196
    16.3 Microcanonical Ensemble 197
    16.4 Connection with Thermodynamics 199
    16.5 Grand Canonical Ensemble 200
    16.6 Finite-Temperature Ideal Fermi Gas 202
    16.7 Fermi Systems in Astrophysics 205
    16.7.1 Degenerate Electron Gas in White Dwarf Stars 205
    16.7.2 Neutron Stars 207
    16.8 Finite-Temperature Ideal Bose Gas: Black Body Radiation 210
    16.8.1 Spectral Decomposition of the Electromagnetic Field 210
    16.8.2 Quantization of the Electromagnetic Field: Photon Gas 211
    16.8.3 Black-Body Radiation from the Classical Point of View 213
    16.9 Complement to Sec.16.5: Grand Canonical Probability 214
    16.10 Complement to Sec.16.7: Newtonian Hydrostatic Equilibrium 215
    16.11 Notes and References 216
    16.12 Problems 217
    Chapter 17 Semi-Classical Limit 218
    17.1 Wigner and Weyl Transforms 218
    17.2 Ehrenfest Theorem Revisited 220
    17.3 Semiclassical Limit of the HF Approximation 221
    17.4 Complement to Sec.17.2 223
    17.5 Notes and References 224
    17.6 Problems 225
    Chapter 18 Collective Modes in Atomic and Nuclear Systems 226
    18.1 Collective Modes in Fermi Systems 226
    18.1.1 Quantum First Sound 227
    18.1.2 Zero Sound 228
    18.1.3 Nuclear Collective Modes 230
    18.2 Notes and References 237
    18.3 Problems 237
    Appendix A Vectors and Operators 239
    A.1 Multidimensional Vector Spaces 239
    A.2 Hilbert Space H 240
    A.3 Operators 241
    A.3.1 Properties of Operators 241
    A.3.2 Projection Operators 242
    A.4 Eigenvalue Problem 243
    A.5 Representation of Vectors and Operators 243
    A.5.1 Matrix Representation 243
    A.5.2 Matrix Representation of Vectors and Operators 244
    A.5.3 Eigenvalue Problem in Matrix Form 245
    A.6 Continuous Spectrum and Dirac δ-function 245
    Appendix B Special Functions in Quantum Mechanics 247
    B.1 Orbital Angular Momentum in Polar Coordinates 247
    B.2 Spherical Harmonics and Legendre Polynomials 248
    B.3 Spherical Bessel Functions 250
    B.4 Hermite Polynomials 252
    B.5 Laguerre Polynomials 253
    Appendix C Coupling of Angular Momenta 254
    C.1 Clebsch-Gordan Coefficients 254
    C.2 Tensor Operators: Wigner-Eckart Theorem 256
    C.3 Projection Theorem 258
    Appendix D Mathematical Complements 261
    D.1 Fourier Transform and Convolution Theorem 261
    D.2 The Green Function Formalism 262
    D.3 The Residue Theorem 263
    Physical Constants 266
    Units of Measurement 268
    Bibliography 269
    Subject Index 270
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