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《理论物理中的Mathematica:电动力学,量子力学,广义相对论和分形(第二版)(英文)》由科学出版社出版。
作者简介
作者：（美国）鲍曼（G.Baumann）
目录
Volume 1
Preface
1 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
1.1.5 Graphics
1.1.6 Programming
2 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 oflnertia
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 Programms
3 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 Scatterirtg 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 ofthe KdV Equation
3.7.2 Conservation Laws for the KdV Equation
3.7.3 Numerical Solution of the KdV Equation
References
Index
Volume 2
Preface
4 Electrodynamics
4.1 Introduction
4.2 Potential and Electric Field of Discrete Charge Distributions
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 Trap
5 Quantum Mechanics
5.1 Introduction
5.2 The Schrodinger Equation
5.3 One—Dimensiona 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 Thermodynamic Properties
5.7.2 Calculation of the Classical SVC Bc（T） for the （2n— n） —Potential
5.7.3 Quantum Mechanical Corrections Bq1（T） and Bq2（T） of the SVC
5.7.4 Shape Dependence of the Boyle Temperature
5.7.5 The High—Temperature Partition Function for Diatomic Molecules
5.8 Exercises
5.9 Packagesand Programs
5.9.1 Quantum Well
5.9.2 Harmonic Oscillator
5.9.3 Anharmonic Oscillator
5.9.4 Central Field
6 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 Kfuskal Coordinates
6.6 The Reissner—Nordstrom Solution for a Charged Mass Point
6.7 Exercises
6.8 Packages and Programs
6.8.1 Euler Lagrange Equations
6.8.2 Perihelion Shift
6.8.3 Light Bending
7 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 Calculus
Appendix
A.1 Program Installation
A.2 Glossary of Files and Functions
A.3 Mathemarica Functions
References
Index
文摘
版权页：
插图：
Especially for the （m—n）—Lennard—Jones potential （abbreviated by （m，n）—LJ） analytical results in terms of series expansions with the г function have been given in （5.12）.It was pointed out， however，by several authors， also in recent textbooks that for the potencial， especially the 12—6， no closed solution exists.That this statement is not correct will be shown subsequently in the sketch on analytical approaches to the SVC.What is lacking， however， is a consistent derivation of the SVC， its quantum corrections， and its temperature derivatives from one integral.The present section aims at such a unified derivation.Also， other results in the Iiterature will be reduced to these results.
5.7.1 The SVC and Its Relation to Thermodynamic Properties
The necessary formulas for the SVC and its quantum corrections are collected to show the importance for thermodynamic functions.The virial equation of state was given in Eq.（5.7.104）.A knowledge of the virial coefficients and their temperature dependence describes the pVT behavior of the gas completely， if one assumes the convergence of the series.
《理论物理中的Mathematica:电动力学,量子力学,广义相对论和分形(第二版)(英文)》由科学出版社出版。
作者简介
作者：（美国）鲍曼（G.Baumann）
目录
Volume 1
Preface
1 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
1.1.5 Graphics
1.1.6 Programming
2 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 oflnertia
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 Programms
3 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 Scatterirtg 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 ofthe KdV Equation
3.7.2 Conservation Laws for the KdV Equation
3.7.3 Numerical Solution of the KdV Equation
References
Index
Volume 2
Preface
4 Electrodynamics
4.1 Introduction
4.2 Potential and Electric Field of Discrete Charge Distributions
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 Trap
5 Quantum Mechanics
5.1 Introduction
5.2 The Schrodinger Equation
5.3 One—Dimensiona 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 Thermodynamic Properties
5.7.2 Calculation of the Classical SVC Bc（T） for the （2n— n） —Potential
5.7.3 Quantum Mechanical Corrections Bq1（T） and Bq2（T） of the SVC
5.7.4 Shape Dependence of the Boyle Temperature
5.7.5 The High—Temperature Partition Function for Diatomic Molecules
5.8 Exercises
5.9 Packagesand Programs
5.9.1 Quantum Well
5.9.2 Harmonic Oscillator
5.9.3 Anharmonic Oscillator
5.9.4 Central Field
6 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 Kfuskal Coordinates
6.6 The Reissner—Nordstrom Solution for a Charged Mass Point
6.7 Exercises
6.8 Packages and Programs
6.8.1 Euler Lagrange Equations
6.8.2 Perihelion Shift
6.8.3 Light Bending
7 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 Calculus
Appendix
A.1 Program Installation
A.2 Glossary of Files and Functions
A.3 Mathemarica Functions
References
Index
文摘
版权页：
插图：
Especially for the （m—n）—Lennard—Jones potential （abbreviated by （m，n）—LJ） analytical results in terms of series expansions with the г function have been given in （5.12）.It was pointed out， however，by several authors， also in recent textbooks that for the potencial， especially the 12—6， no closed solution exists.That this statement is not correct will be shown subsequently in the sketch on analytical approaches to the SVC.What is lacking， however， is a consistent derivation of the SVC， its quantum corrections， and its temperature derivatives from one integral.The present section aims at such a unified derivation.Also， other results in the Iiterature will be reduced to these results.
5.7.1 The SVC and Its Relation to Thermodynamic Properties
The necessary formulas for the SVC and its quantum corrections are collected to show the importance for thermodynamic functions.The virial equation of state was given in Eq.（5.7.104）.A knowledge of the virial coefficients and their temperature dependence describes the pVT behavior of the gas completely， if one assumes the convergence of the series.
| ISBN | 9787030313379 |
|---|---|
| 出版社 | 科学出版社 |
| 作者 | 鲍曼 (G.Baumann) |
| 尺寸 | 5 |