量子力学

Preface
1 Classical Mechanics
1.1 Newton's Laws, the Action, and the Hamiltonian
1.1.1 Newton's Law and Lagrange's Equations
1.1.2 Hamilton's Principle
1.1.3 Canonical Momenta and the Hainiltonian Formulation .
1.2 Classical Space-Time Symmetries
1.2.1 The Space-Time Transformations
1.2.2 Translations
1.2.3 Rotations
1.2.4 Rotation Matrices
1.2.5 Symmetries and Conservation Laws
Problems
2 Fundamentals of Quantum Mechanics
2.1 The Superposition Principle
2.1.1 The Double-Slit Experiment
2.1.2 The Stern-Gerlach Experiment
2.2 The Mathematical Language of Quantum Mechanics
2.2.1 Vector Spaces
2.2.2 The Probability Interpretation
2.2.3 Linear Operators
2.2.4 Observables
2.2.5 Examples
2.3 Continuous Eigenvalues
2.3.1 The Dirac Delta Function
2.3.2 Continuous Observables
2.3.3 Fourier's Theorem and Representations of Q(x)
2.4 Canonical Commutators and the SchrSdinger Equation
2.4.1 The Correspondence Principle
2.4.2 The Canonical Commutation Relations
2.4.3 Planck's Constant
2.5 Quantum Dynamics
2.5.1 The Time-Translation Operator
2.5.2 The Heisenberg Picture
2.6 The Uncertainty Principle
2.7 Wave Functions
2.7.1 Wave Functions in Coordinate Space
2.7.2 Momentum and Translations
2.7.3 SchrSdinger's Wave Equation
2.7.4 Time-Dependent Free Particle Wave Functions
Problems
3 Stationary States
3.1 Elementary Examples
3.1.1 States with Definite Energy
3.1.2 A Two-State System
3.1.3 One-Dimensional Potential Problems
　3.2 The Harmonic Oscillator
3.2.1 The Spectrum
3.2.2 Matrix Elements
3.2.3 The Ground-State Energy
3.2.4 Wave Functions
　3.3 Spherically Symmetric Potentials and Angular Momentum
3.3.1 Spherical Symmetry
3.3.2 Orbital Angular Momentum as a Differential Operator
3.3.3 The Angular Momentum Commutator Algebra
3.3.4 Classification of the States
　3.4 Spherically Symmetric Potentials: Wave Functions
3.4.1 Spherical Coordinates and Spherical Harmonics
3.4.2 The Radial Wave Equation
　3.5 Hydrogenlike Atoms
3.5.1 The Symmetries
3.5.2 The Energy Spectrum
3.5.3 The Radial Wave Functions
　Problems
4　Symmetry Transformations on States
4.1 Introduction
4.1.1 Symmetries and Transformations
4.1.2 Groups of Transformations
4.1.3 Classical and Quantum Symmetries
4.2 The Rotation Group and Algebra
4.2.1 Representations of Groups
4.2.2 Representations of the Generators of Rotations
4.2.3 Generators in an Arbitrary Direction
4.2.4 Commutators of the Generators
4.2.5 Explicit Form of the Finite Dimensional Representations
4.2.6 Summary
4.3 Spin and Rotations in Quantum Mechanics
4.3.1 Rotations and Spinless Particles
4.3.2 Spin
4.3.3 The Spin-Zero Representation
4.3.4 The Spin-Half Representation
4.3.5 Euler Angles
4.3.6 The Spin-One Representation
4.3.7 Arbitrary j
4.4 Addition of Angular Momenta
4.4.1 Spin and Orbital Angular Momentum
4.4.2 Two Simple Examples
　……
5　Symmetry Transformations on operators
6 Interlude
7 Approximation methods for bound states
8 Potential scattering
9 Transitions
10 Further topics in quantum dynamics
11 The quantized electromagnetic field
12 Relativistic wave equations
13 Identical particles
APPENDICES
A Mathematical tools
B Rotation Matrices
C SU（3）
D Reference
Index