Chapter 1 Mathematical Tools of Quantum Mechanics
1.1 The Hilbert Space
1.2 Dual Spaces and the Dirac Notation
1.3 Operators
1.4 Self-adjoint Operators and Eigen-problem
1.5 Representation in Discrete Bases
1.6 Representation in Continues Bases
1.7 Matrix and Wave Function
1.8 Direct Product and Direct Sum
1.9 Exercises
Chapter 2 Fundamentals of Quantum Mechanics
2.1 The Basic Postulates of Quantum Mechanics
2.2 The State of a System
2.3 Observables and Operators
2.4 Measurement in Quantum Mechanics
2.5 Time Evolution of the System's State
2.6 Symmetries and Conservation Laws
2.7 State Operator
2.8 Three Pictures of Quantum Mechanics
2.9 Connecting Quantum to Classical Mechanics
2.10 Approximation Methods Ⅰ —— The Variational Method
2.11 Approximation Methods Ⅱ —— the WKB Method
2.12 Exercises
Chapter 3 Second Quantization
3.1 Identical Particles, Many-Particle States and Permutation Symmetry
3.2 Bosons
3.3 Fermions
3.4 Field Theory
3.5 Momentum Representation
3.6 Noninteracting Fermions
3.7 Ground State Energy and Elementary Theory of the Electron Gas
*3.8 Hartree-Fock Equations for Atoms
3.9 Free Bosons
*3.10 Weakly Interacting, Dilute Bose Gas
3.11 Exercises
Chapter 4 Coherent States and Squeezed States
4.1 Four Representations of Quantum States
4.2 Coherent States
4.3 The Quasi–classical Interpretation of Coherent States
4.4 Coordinate Representation in Terms of Displacement Operator
4.5 Coherent States Vector Algebra
4.6 Squeezed States
4.7 Exercises
Chapter 5 Green's Functions and Scattering Theory
5.1 Time-independent Green's Functions
5.2 Time-dependent Green's Functions
5.3 Green's Functions and Perturbation Theory
5.4 Scattering Theory Ⅰ —— Scattering Operators and Born Approximation
5.5 Scattering Theory Ⅱ —— Partial Wave
Chapter 6 Geometric Phases
6.1 Introduction
6.2 Quantal Phase Factors for Adiabatic Changes
6.3 Adiabatic Approximation
6.4 Berry's Adiabatic Phase
