量子力学

Preface1 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 Problems2 Fundamentals of Quantum Mechanics 2.1 The Superposition Principle

Preface1 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 Problems2 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 Problems3 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　Problems4　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 operators6 Interlude7 Approximation methods for bound states8 Potential scattering9 Transitions10 Further topics in quantum dynamics11 The quantized electromagnetic field12 Relativistic wave equations13 Identical particlesAPPENDICES A Mathematical tools B Rotation Matrices C SU（3） D ReferenceIndex

本书具有起点较高，内容丰富，分析深刻等特。强调对称性在量子力学中的重要性，特别是仔细分析了转动对称性与一般角动量的深刻联系；详细讨论了作为前沿科学研究基础的路径积分和电磁场量子化等。书中数学推导比较详细，便于读者自己验证推算量子力学基本内容。