理论物理中的Mathematica：电动力学，量子力学，广义相对论和分形

Volume IPreface1 Introduction 1.1 Basics 1.1.1 Structure of Mathematica 1.1.2 Interactive Use of Mathematica 1.1.3 Symbolic Calculations 1.1.4 Numerical Calculations I.1.5 Graphics 1.1.6 Programming2 Classical Mechanics 2.1 Introduction 2.2 Mathematical Tools 2.2.1 Introduction 2.2.2 Coordinates 2.2.3 Coordinate Transformations and Matrices 2.2.4 Scalars 2.2.5 Vectors 2.2.6 Tensors 2.2.7 Vector Products 2.2.8 Derivatives 2.2.9 Integrals 2.2.10 Exercises 2.3 Kinematics 2.3.1 Introduction 2.3.2 Velocity 2.3.3 Acceleration 2.3.4 Kinematic Examples 2.3.5 Exercises 2.4 Newtonian Mechanics 2.4.1 Introduction 2.4.2 Frame of Reference 2.4.3 Time 2.4.4 Mass 2.4.5 Newton's Laws 2.4.6 Forces in Nature 2.4.7 Conservation Laws 2.4.8 Application of Newton's Second Law 2.4.9 Exercises 2.4.10 Packages and Programs 2.5 Central Forces 2.5.1 Introduction 2.5.2 Kepler's Laws 2.5.3 Central Field Motion 2.5.4 Two-Particle Collisons and Scattering 2.5.5 Exercises 2.5.6 Packages and Programs 2.6 Calculus of Variations 2.6.1 Introduction 2.6.2 The Problem of Variations 2.6.3 Euler's Equation 2.6.4 Euler Operator 2.6.5 Algorithm Used in the Calculus of Variations 2.6.6 Euler Operator for q Dependent Variables 2.6.7 Euler Operator for q + p Dimensions 2.6.8 Variations with Constraints 2.6.9 Exercises 2.6.10 Packages and Programs 2.7 Lagrange Dynamics 2.7.1 Introduction 2.7.2 Hamilton's Principle Hisorical Remarks 2.7.3 Hamilton's Principle 2.7.4 Symmetries and Conservation Laws 2.7.5 Exercises 2.7.6 Packages and Programs 2.8 Hamiltonian Dynamics 2.8.1 Introduction 2.8.2 Legendre Transform 2.8.3 Hamilton's Equation of Motion 2.8.4 Hamilton's Equations and the Calculus of Variation 2.8.5 Liouville's Theorem 2.8.6 Poisson Brackets 2.8.7 Manifolds and Classes 2.8.8 Canonical Transformations 2.8.9 Generating Functions 2.8.10 Action Variables 2.8.11 Exercises 2.8.12 Packages and Programs 2.9 Chaotic Systems 2.9.1 Introduction 2.9.2 Discrete Mappings and Hamiltonians 2.9.3 Lyapunov Exponents 2.9.4 Exercises 2.10 Rigid Body 2.10.1 Introduction 2.10.2 The Inertia Tensor 2.10.3 The Angular Momentum 2.10.4 Principal Axes of Inertia 2.10.5 Steiner's Theorem 2.10.6 Euler's Equations of Motion 2.10.7 Force-Free Motion of a Symmetrical Top 2.10.8 Motion of a Symmetrical Top in a Force Field 2.10.9 Exercises 2.10.10 Packages and Programms3 Nonlinear Dynamics 3.1 Introduction 3.2 The Korteweg-de Vries Equation 3.3 Solution of the Korteweg-de Vries Equation 3.3.1 The Inverse Scattering Transform 3.3.2 Soliton Solutions of the Korteweg-de Vries Equation 3.4 Conservation Laws of the Korteweg--de Vries Equation 3.4.1 Definition of Conservation Laws 3.4.2 Derivation of Conservation Laws 3.5 Numerical Solution of the Korteweg--de Vries Equation 3.6 Exercises 3.7 Packages and Programs 3.7.1 Solution of the KdV Equation 3.7.2 Conservation Laws for the KdV Equation 3.7.3 Numerical Solution of the KdV Equation References IndexVolume IIPreface4 Electrodynamics 4.1 Introduction 4.2 Potential and Electric Field of Discrete ChargeDistributions 4.3 Boundary Problem of Electrostatics 4.4 Two Ions in the Penning Trap 4.4.1 The Center of Mass Motion 4.4.2 Relative Motion of the Ions 4.5 Exercises 4.6 Packages and Programs 4.6.1 Point Charges 4.6.2 Boundary Problem 4.6.3 Penning Trap5 Quantum Mechanics 5.1 Introduction 5.2 The Schr6dinger Equation 5.3 One-Dimensional Potential 5.4 The Harmonic Oscillator 5.5 Anharmonic Oscillator 5.6 Motion in the Central Force Field 5.7 Second Virial Coefficient and Its Quantum Corrections 5.7.1 The SVC and Its Relation to ThermodynamicProperties 5.7.2 Calculation of the Classical SVC Be(T) for the(2 n - n)-Potential 5.7.3 Quantum Mechanical Corrections Bqt(T) andBq2 (T) of theSVC 5.7.4 Shape Dependence of the Boyle Temperature 5.7.5 The High-Temperature Partition Function for DiatomicMolecules 5.8 Exercises 5.9 Packages and Programs 5.9.1 QuantumWell 5.9.2 HarmonicOscillator 5.9.3 AnharmonicOsciilator 5.9.4 CentralField6 General Relativity 6.1 Introduction 6.2 The Orbits in General Relativity 6.2.1 Quasielliptic Orbits 6.2.2 Asymptotic Circles 6.3 Light Bending in the Gravitational Field 6.4 Einstein's Field Equations (Vacuum Case) 6.4.1 Examples for Metric Tensors 6.4.2 The Christoffel Symbols 6.4.3 The Riemann Tensor 6.4.4 Einstein's Field Equations 6.4.5 The Cartesian Space 6.4.6 Cartesian Space in Cylindrical Coordinates 6.4.7 Euclidean Space in Polar Coordinates 6.5 The Schwarzschild Solution 6.5.1 The Schwarzschild Metric in Eddington-Finkelstein Form 6.5.2 Dingle's Metric 6.5.3 Schwarzschild Metric in Kruskal Coordinates 6.6 The Reissner-Nordstrom Solution for a Charged Mass Point 6.7 Exercises 6.8 Packages and Programs 6.8.1 EulerLagrange Equations 6.8.2 PerihelionShift 6.8.3 LightBending7 Fractals 7.1 Introduction 7.2 Measuring a Borderline 7.2.1 Box Counting 7.3 The Koch Curve 7.4 Multifractals 7.4.1 Multifractals with Common Scaling Factor 7.5 The Renormlization Group 7.6 Fractional Calculus 7.6.1 Historical Remarks on Fractional Calculus 7.6.2 The Riemann-Liouville Calculus 7.6.3 Mellin Transforms 7.6.4 Fractional Differential Equations 7.7 Exercises 7.8 Packages and Programs 7.8.1 Tree Generation 7.8.2 Koch Curves 7.8.3 Multifactals 7.8.4 Renormalization 7.8.5 Fractional CalculusAppendix A.1 Program Installation A.2 Glossary of Files and Functions A.3 Mathematica FunctionsReferencesIndex