理论物理中的“Mathematica” 电动力学，量子力学，广义相对论和分形 影印版PDF|Epub|txt|kindle电子书版本网盘下载

理论物理中的“Mathematica” 电动力学，量子力学，广义相对论和分形 影印版PDF格式电子书版下载

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VolumeⅠ1

1 Introduction1

1.1 Basics1

1.1.1 Structure of Mathematica2

1.1.2 Interactive Use of Mathematica4

1.1.3 Symbolic Calculations6

1.1.4 Numerical Calculations11

1.1.5 Graphics13

1.1.6 Programming23

2 Classical Mechanics31

2.1 Introduction31

2.2 Mathematical Tools35

2.2.1 Introduction35

2.2.2 Coordinates36

2.2.3 Coordinate Transformations and Matrices38

2.2.4 Scalars54

2.2.5 Vectors57

2.2.6 Tensors59

2.2.7 Vector Products64

2.2.8 Derivatives69

2.2.9 Integrals73

2.2.10 Exercises74

2.3 Kinematics76

2.3.1 Introduction76

2.3.2 Velocity77

2.3.3 Acceleration81

2.3.4 Kinematic Examples82

2.3.5 Exercises94

2.4 Newtonian Mechanics96

2.4.1 Introduction96

2.4.2 Frame of Reference98

2.4.3 Time100

2.4.4 Mass101

2.4.5 Newton's Laws103

2.4.6 Forces in Nature106

2.4.7 Conservation Laws111

2.4.8 Application of Newton's Second Law118

2.4.9 Exercises188

2.4.10 Packages and Programs188

2.5 Central Forces201

2.5.1 Introduction201

2.5.2 Kepler's Laws202

2.5.3 Central Field Motion208

2.5.4 Two-Particle Collisons and Scattering240

2.5.5 Exercises272

2.5.6 Packages and Programs273

2.6 Calculus of Variations274

2.6.1 Introduction274

2.6.2 The Problem of Variations276

2.6.3 Euler's Equation281

2.6.4 Euler Operator283

2.6.5 Algorithm Used in the Calculus of Variations284

2.6.6 Euler Operator for q Dependent Variables293

2.6.7 Euler Operator for q+p Dimensions296

2.6.8 Variations with Constraints300

2.6.9 Exercises303

2.6.10 Packages and Programs303

2.7 Lagrange Dynamics305

2.7.1 Introduction305

2.7.2 Hamilton's Principle Hisorical Remarks306

2.7.3 Hamilton's Principle313

2.7.4 Symmetries and Conservation Laws341

2.7.5 Exercises351

2.7.6 Packages and Programs351

2.8 Hamiltonian Dynamics354

2.8.1 Introduction354

2.8.2 Legendre Transform355

2.8.3 Hamilton's Equation of Motion362

2.8.4 Hamilton's Equations and the Calculus of Variation366

2.8.5 Liouville's Theorem373

2.8.6 Poisson Brackets377

2.8.7 Manifolds and Classes384

2.8.8 Canonical Ttansformations396

2.8.9 Generating Functions398

2.8.10 Action Variables403

2.8.11 Exercises419

2.8.12 Packages and Programs419

2.9 Chaotic Systems422

2.9.1 Introduction422

2.9.2 Discrete Mappings and Hamiltonians431

2.9.3 Lyapunov Exponents435

2.9.4 Exercises448

2.10 Rigid Body449

2.10.1 Introduction449

2.10.2 The Inertia Tensor450

2.10.3 The Angular Momentum453

2.10.4 Principal Axes of Inertia454

2.10.5 Steiner's Theorem460

2.10.6 Euler's Equations of Motion462

2.10.7 Force-Free Motion of a Symmetrical Top467

2.10.8 Motion of a Symmetrical Top in a Force Field471

2.10.9 Exercises481

2.10.10 Packages and Programms481

3 Nonlinear Dynamics485

3.1 Introduction485

3.2 The Korteweg-de Vries Equation488

3.3 Solution of the Korteweg-de Vries Equation492

3.3.1 The Inverse Scattering Transform492

3.3.2 Soliton Solutions of the Korteweg-de Vries Equation498

3.4 Conservation Laws of the Korteweg-de Vries Equation505

3.4.1 Definition of Conservation Laws506

3.4.2 Derivation of Conservation Laws508

3.5 Numerical Solution of the Korteweg-de Vries Equation511

3.6 Exercises515

3.7 Packages and Programs516

3.7.1 Solution of the KdV Equation516

3.7.2 Conservation Laws for the KdV Equation517

3.7.3 Numerical Solution of the KdV Equation518

References521

Index529

VolumeⅡ545

4 Electrodynamics545

4.1 Introduction545

4.2 Potential and Electric Field of Discrete Charge Distributions548

4.3 Boundary Problem of Electrostatics555

4.4 Two Ions in the Penning Trap566

4.4.1 The Center of Mass Motion569

4.4.2 Relative Motion of the Ions572

4.5 Exercises577

4.6 Packages and Programs578

4.6.1 Point Charges578

4.6.2 Boundary Problem581

4.6.3 Penning Trap582

5 Quantum Mechanics587

5.1 Introduction587

5.2 The Schr？dinger Equation590

5.3 One-Dimensional Potential595

5.4 The Harmonic Oscillator609

5.5 Anharmonic Oscillator619

5.6 Motion in the Central Force Field631

5.7 Second Virial Coefficient and Its Quantum Corrections642

5.7.1 The SVC and Its Relation to Thermodynamic Properties644

5.7.2 Calculation of the Classical SVC Bc(T)for the(2n-n)-Potential646

5.7.3 Quantum Mechanical Corrections Bq1(T)and Bq2(T)of the SVC655

5.7.4 Shape Dependence of the Boyle Temperature680

5.7.5 The High-Temperature Partition Function for Diatomic Molecules684

5.8 Exercises687

5.9 Packages and Programs688

5.9.1 QuantumWell688

5.9.2 HarmonicOscillator693

5.9.3 AnharmonicOscillator695

5.9.4 CentralField698

6 General Relativity703

6.1 Introduction703

6.2 The Orbits in General Relativity707

6.2.1 Quasielliptic Orbits713

6.2.2 Asymptotic Circles719

6.3 Light Bending in the Gravitational Field720

6.4 Einstein's Field Equations(Vacuum Case)725

6.4.1 Examples for Metric Tensors727

6.4.2 The Christoffel Symbols731

6.4.3 The Riemann Tensor731

6.4.4 Einstein's Field Equations733

6.4.5 The Cartesian Space734

6.4.6 Cartesian Space in Cylindrical Coordinates736

6.4.7 Euclidean Space in Polar Coordinates737

6.5 The Schwarzschild Solution739

6.5.1 The Schwarzschild Metric in Eddington-Finkelstein Form739

6.5.2 Dingle's Metric742

6.5.3 Schwarzschild Metric in Kruskal Coordinates748

6.6 The Reissner-Nordstrom Solution for a Charged Mass Point752

6.7 Exercises759

6.8 Packages and Programs761

6.8.1 EulerLagrange Equations761

6.8.2 PerihelionShifi762

6.8.3 LightBending767

7 Fractals773

7.1 Introduction773

7.2 Measuring a Borderline776

7.2.1 Box Counting781

7.3 The Koch Curve790

7.4 Multifractals795

7.4.1 Muitifractals with Common Scaling Factor798

7.5 The Renormlization Group801

7.6 Fractional Calculus809

7.6.1 Historical Remarks on Fractional Calculus810

7.6.2 The Riemann-Liouville Calculus813

7.6.3 Mellin Transforms830

7.6.4 Fractional Differential Equations856

7.7 Exercises883

7.8 Packages and Programs883

7.8.1 Tree Generation883

7.8.2 Koch Curves886

7.8.3 Multifactals892

7.8.4 Renormalization895

7.8.5 Fractional Calculus897

Appendix899

A.1 Program Installation899

A.2 Glossary of Files and Functions900

A.3 Mathematica Functions910

References923

Index931