內容大鋼
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
Chapter 1 Space-Time Symmetries and Classical Observables
1.1 Hamilton's Equations
1.2 Space-Time Symmetries and Conservation of Dynamical Variables
1.3 Canonical Transformations and Space-Time Symmetries
1.4 Notes and References
1.5 Problems
Chapter 2 Superposition Principle
2.1 An Historic Experiment
2.2 Wave-like Behaviour of Particles
2.3 Particle-like Behaviour of Waves
2.4 The Stern-Gerlach Experiment
2.5 Notes and References
2.6 Problems
Chapter 3 States and Dynamical Variables
3.1 States of a Quantum System as Vectors of Hilbert Space ..,
3.2 Observables as Operators in Hilbert Space
3.3 General Properties of Quantum Observables
3.4 Unitary Transformations
3.5 Notes and References
3.6 Problems
Chapter 4 Space Translations and Momentum
4.1 Wave Function and Position Operator
4.2 Space Translations
4.3 Momentum as a Generator of Infinitesimal Translations ...
4.4 Free Particle in a Box
4.5 Heisenberg Uncertainty Relations
4.6 Notes and References
4.7 Problems
Chapter 5 Elementary Phenomena
5.1 Double-Slit Interference
5.2 Diffraction Grating
5.3 Double-Layer Reflection
5.4 Scattering of Identical Particles
5.5 Notes and References
5.6 Problems
Chapter 6 Space Rotations and Angular Momentum
6.1 Space Rotations
6.2 Orbital Angular Momentum as Generator of Infinitesimal Rotations
6.3 Properties of the Angular Momentum
6.4 Orbital Angular Momentum in Polar Coordinates
6.5 Reflection of Axes and Parity
6.6 Spin
6.7 The Rigid Rotor
6.8 Complement to Sec.6.1 : Infinitesimal Space Rotations
6.9 Notes and References
6.10 Problems
Chapter 7 Time Translations and Hamiltonian
7.1 Time Evolution Operator
7.2 Equations of Motion
7.3 Stationary SchrSdinger Equation
7.3.1 SchrSdinger Equation for Potential Wells
7.3.2 Attractive Well: Vo < 0
7.3.3 Repulsive Well: V0 > 0
7.3.4 Potential Barrier: 0 < E < V0
7.3.5 Potential Barrier: E > V0 > 0
7.4 Problems
Chapter 8 Harmonic Oscillations
8.1 Quantum Harmonic Oscillator
8.1.1 Eigenfunctions of the Harmonic Oscillator
8.2 Vibrations of a Crystal Lattice
8.2.1 Small Oscillations in Classical Approach
8.2.2 Small Oscillations in Quantum Approach
8.3 Three-Dimensional Harmonic Oscillator
8.4 Notes and References
8.5 Problems
Chapter 9 Approximations to Schr~idinger's Equation
9.1 Perturbation Theory
9.1.1 Non-Degenerate Case
9.1.2 Degenerate Case
9.2 Variational Approach
9.3 Perturbation vs. Variational Approximations for 4He
9.3.1 Perturbation Method
9.3.2 Variational Estimate
9.4 Problems
Chapter 10 Time-Dependent Equations of Motion
10.1 Heisenberg Representation
10.2 Two-Level Quantum System
10.2.1 Unperturbed Hamiltonian
10.2.2 Perturbation Potential
10.2.3 Time-Dependent Hamiltonian
10.3 Relationship between Symmetries and Conservation Theorems
10.4 Classical Limit: Ehrenfest Theorem
10.5 Particle Detection in Scattering Processes
10.6 Problems
Chapter 11 Time-Dependent Perturbation Theory
11.1 Interaction Representation
11.2 Electron Transitions in Atoms
11.3 Dipole Approximation
11.4 Slow vs. Fast Processes
11.5 Complement to Sec.11.2: Interaction of Charged Particles with the Electromagnetic Field
11.6 Notes and References
11.7 Problems
Chapter 12 Two-Body Problem: Bound States
12.1 Central Potential
12.2 Hydrogen Atom
12.3 Isospin
12.4 Ground State of the Deuteron
12.5 Complement to Sec.12.4: Tensor Interaction
12.6 Notes and References
12.7 Problems
Chapter 13 Two-Body Problem: Scattering States
13.1 Lippmann-Schwinger Equation
13.2 Asymptotic Form of the Continuum States
13.3 Solving the Lippmann-Schwinger Equation
13.4 Elastic Scattering Cross Section
13.4.1 Born Approximation for the Elastic Scattering Cross Section
13.4.2 Nuclear and Coulomb Potential
13.4.3 Electron Scattering and Nuclear Density
13.5 Partial-Wave Analysis
13.6 Low-Energy Scattering and Bound States
13.7 Nuclear Interaction from Nucleon-Nucleon Scattering
13.8 Notes and References
13.9 Problems
Chapter 14 Many-Body Systems
14.1 Systems of Identical Particles
14.2 The Hartree-Fock Approximation
14.3 Atomic Structure
14.4 Nuclear Structure
14.4.1 The Nuclear Shell Model
14.4.2 Liquid Drop Model and Nuclear Matter
14.4.3 Microscopic Approaches
14.5 Complement to Sec.14.2: Second Quantization
14.6 Complement to Sec.14.4.1: Isotropic 3-Dimensional Harmonic Oscillator
14.7 Notes and References
14.8 Problems
Chapter 15 The Dirac Equation
15.1 The Klein-Gordon Equation
15.2 Dirac's Equation
15.2.1 Diagonalization of the Hamiltonian
15.2.2 The Spin Variable
15.3 Covariant Form of the Dirac Equation
15.4 The Spin-Orbit Interaction
15.5 Complement to Sec.15.4: Semi-Classical Hamiltonian
15.6 Notes and References
15.7 Problems
Chapter 16 Homogeneous Many-Body Systems
16.1 Gibbs Statistical Approach
16.2 Time Average and Statistical Average
16.3 Microcanonical Ensemble
16.4 Connection with Thermodynamics
16.5 Grand Canonical Ensemble
16.6 Finite-Temperature Ideal Fermi Gas
16.7 Fermi Systems in Astrophysics
16.7.1 Degenerate Electron Gas in White Dwarf Stars
16.7.2 Neutron Stars
16.8 Finite-Temperature Ideal Bose Gas: Black Body Radiation
16.8.1 Spectral Decomposition of the Electromagnetic Field
16.8.2 Quantization of the Electromagnetic Field: Photon
16.8.3 Black-Body Radiation from the Classical Point of View
16.9 Complement to Sec.16.5 : Grand Canonical Probability
16.10 Complement to Sec.16.7 : Newtonian Hydrostatic Equilibrium
16.11 Notes and References
16.12 Problems
Chapter 17 Semi-Classical Limit
17.1 Wigner and Weyl Transforms
17.2 Ehrenfest Theorem Revisited
17.3 Semiclassical Limit of the HF Approximation
17.5 Notes and References
17.6 Problems
Chapter 18 Collective Modes in Atomic and Nuclear Systems
18.1 Collective Modes in Fermi Systems
18.1.1 Quantum First Sound
18.1.2 Zero Sound
18.1.3 Nuclear Collective Modes
18.2 Notes and References
18.3 Problems
Appendix A Vectors and Operators
A.1 Multidimensional Vector Spaces
A.2 Hilbert Space
A.3 Operators
A.3.1 Properties of Operators
A.3.2 Projection Operators
A.4 Eigenwlue Problem
A.5 Representation of Vectors and Operators
A.5.1 Matrix Representation
A.5.2 Matrix Representation of Vectors and Operators
A.5.3 Eigenvalue Problem in Matrix Form
A.6 Continuous Spectrum and Dirac b-function
Appendix B Special Functions in Quantum Mechanics.-.
B.1 Orbital Angular Momentum in Polar Coordinates
B.2 Spherical Harmonics and Legendre Polynomials
B.3 Spherical Bessel Functions
B.4 Hermite Polynomials
B.5 Laguerre Polynomials
Appendix C Coupling of Angular Momenta
C.1 Clebsch-Gordan Coefficients
C.2 Tensor Operators: Wigner-Eckart Theorem
C.3 Projection Theorem
Appendix D Mathematical Complements
D.1 Fourier Transform and Convolution Theorem
D.2 The Green Function Formalism
D.3 The Residue Theorem
Physical Constants
Units of Measurement
Bibliography
Subject Index
[