量子力學

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

量子力學是現代物質科學的支柱。目前，量子力學不僅是物理學系學生最重要的理論課程，而且是許多工程學科進行源頭創新的基礎。在清華大學，不少的工科系專門開設量子力學課。

Ernest.Abers的《量子力學》具有起點較高，內容豐富，分析深刻等特點。例如︰講述量子力學之前，在第1章先復習分析力學的哈密頓形式，便于學生掌握量子動力學的表述形式︰強調對稱性在量子力學中的重要性，特別是仔細分析了轉動對稱性與一般角動量的深刻聯系；詳細討論了作為前沿科學研究基礎的路徑積分和電磁場量子化；等等。書中數學推導比較詳細，便于讀者自己驗證推算量子力學基本內容。

本書適合物理系各專業的學生，也可作為工科學或工程研究人員學習量子力學的參考書。學習之前最好已修近代物理、分析力學與線性代數課程。