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【内容】
《计算物理学》（第2版）是一部非常规范的高等计算物理教科书。内容包括用于计算物理学中的重要算法的简洁描述。本书第1部分介绍数值方法的基本理论，其中包含大量的习题和仿真实验。本书第2部分主要聚焦经典和量子系统的仿真等内容。读者对象：计算物理等相关专业的研究生。
【目录】
Part Ⅰ Numerical Methods
1 Error Analysis
1.1 Machine Numbers and Rounding Errors
1.2 Numerical Errors of Elementary Floating Point Operations
1.2.1 Numerical Extinction
1.2.2 Addition
1.2.3 Multiplication
1.3 Error Propagation
1.4 Stability of Iterative Algorithms
1.5 Example： Rotation
1.6 Truncation Error
1.7 Problems
2 Interpolation
2.1 Interpolating Functions
2.2 Polynomial Interpolation
2.2.1 Lagrange Polynomials
2.2.2 Barycentric Lagrange Interpolation
2.2.3 Newton's Divided Differences
2.2.4 Neville Method
2.2.5 Error of Polynomial Interpolation
2.3 Spline Interpolation
2.4 Rational Imerpolation
2.4.1 Pade Approximant
2.4.2 Barycentric Rational Interpolation
2.5 Multivariate Interpolation
2.6 Problems
3 Numerical Differentiahon
3.1 One—Sided Difference Quotient
3.2 Central Difference Quotient
3.3 Extrapolation Methods
3.4 Higher Derivatives
3.5 Partial Derivatives of Multivariate Functions
3.6 Problems
4 Numerical Integrahon
4.1 Equidistant Sample Points
4.1.1 Closed Newton—Cotes Formulae
4.1.2 Open Newton—Cotes Formulae
4.1.3 Composite Newton—Cotes Rules
4.1.4 Extrapolation Method （Romberg Integration）
4.2 Optimized Sample Points
4.2.1 Clenshaw—Curtis Expressions
4.2.2 Gaussian Integration
4.3 Problems
5 Systems of Inhomogeneous Linear Equations
5.1 Gaussian Elimination Method
5.1.1 Pivoting
5.1.2 Direct LU Decomposition
5.2 QR Decomposition
5.2.1 QR Decomposition by Orthogonalization
5.2.2 QR Decomposition hy Householder Reflections
5.3 Linear Equations wiih Tridiagonal Matrix
5.4 Cyclic Tridiagonal Systems
5.5 Iterative Solution of Inhomogeneous Linear Equations
5.5.1 General Relaxation Method
5.5.2 Jacobi Method
5.5.3 Gauss—Seidel Method
5.5.4 Damping and Successive Over—Relaxation
5.6 Conjugate Gradients
5.7 Matrix Inversion
5.8 Problems
6 Roots and Extremal Points
6.1 Root Finding
6.1.1 Bisection
6.1.2 Regula Falsi （False Position） Method
6.1.3 Newton—Raphson Method
6.1.4 Secant Method
6.1.5 Interpolation
6.1.6 Inverse Interpolation
6.1.7 Combined Methods
6.1.8 Multidimensional Root Finding
6.1.9 Quasi—Newton Methods
6.2 Function Minimization
6.2.1 TheTernary Search Method
6.2.2 The Golden Section Search Method （Brent's Method）
6.2.3 Minimization in Multidimensions
6.2.4 Steepest Descent Method
6.2.5 Conjugate Gradient Method
6.2.6 Newton—Raphson Method
6.2.7 Quasi—Newton Methods
6.3 Problems
Fourier Transformation
7.1 Fourier Integral and Fourier Series
7.2 Discrete Fourier Transformauon
7.2.1 Trigonometric Interpolation
7.2.2 Real Valued Functions
7.2.3 Approximate Continuous Fourier Transformation
7.3 Fourier Transform Algorithms
7.3.1 Goertzel's Algorithm
7.3.2 Fast Fourier Transformation
7.4 Problems
8 Random Numbers and Monte Carlo Methods
8.1 Some Basic Statistics
8.1.1 Probability Density and Cumulative Probability Distribution
8.1.2 Histogram
8.1.3 Expectation Values and Moments
8.1.4 Example： Fair Die
8.1.5 Normal Distribution
8.1.6 Multivariate Distributions
8.1.7 Central Limit Theorem
8.1.8 Example： Binomial Distribution
8.1.9 Average of Repeated Measurements
8.2 Random Numbers
8.2.1 Linear Congruent Mapping
8.2.2 Marsaglia—Zamann Method
8.2.3 Random Numbers with Given Distribution
8.2.4 Examples
8.3 Monte Carlo Integration
8.3.1 Numerical Calculation of π
8.3.2 Calculation of an Integral
8.3.3 More General Random Numbers
8.4 Monte Carlo Method for Thermodynamic Averages
8.4.1 Simple Sampling
8.4.2 Importance Sampling
8.4.3 Metropolis Algorithm
8.5 Problems
9 Eigenvalue Problems
9.1 Direct Solution
9.2 Jacobi Method
9.3 Tridiagonal Matrices
9.3.1 Characteristic Polynomial of a Tridiagonal Matrix
9.3.2 Special Tridiagonal Matrices
9.3.3 The QL Algorithm
9.4 Reduction to a Tridiagonal Matrix
9.5 Large Matrices
9.6 Problems
10 Data Fitting
10.1 LeastSquareFit
10.1.1 Linear Least Square Fit
10.1.2 Linear Least Square Fit with Orthogonalization
10.2 Singular Value Decomposition
10.2.1 Full Singular Value Decomposition
10.2.2 Reduced Singular Value Decomposition
10.2.3 Low Rank Matrix Approximation
10.2.4 Linear Least Square Fit with Singular Value Decomposition
10.3 Problems
11 Discretization of Differential Equations
11.1 Classification of Differential Equations
11.1.1 Linear Second Order PDE
11.1.2 Conservation Laws
11.2 Finite Differences
11.2.1 Finite Differences in Time
11.2.2 Stability Analysis
11.2.3 Method of Lines
11.2.4 Eigenvector Expansion
11.3 Finite Volumes
11.3.1 Discretization of fluxes
11.4 Weighted Residual Based Methods
11.4.1 Point Collocation Method
11.4.2 Sub—domain Method
11.4.3 Least Squares Method
11.4.4 Galerkin Method
11.5 Spectraland Pseudo—spectral Methods
11.5.1 Fourier Pseudo—spectral Methods
11.5.2 Example：Polynomial Approximation
11.6 Finite Elements
11.6.1 One—Dimensional Elements
11.6.2 Two—and Three—Dimensional Elements
11.6.3 One—Dimensional Galerkin FEM
11.7 Boundary Element Method
12 Equations of Motion
12.1 The State Vector
12.2 Time Evolution of the State Vector
12.3 Explicit Forward Euler Method
12.4 Implicit Backward Euler Method
12.5 Improved Euler Methods
12.6 Taylor Series Methods
12.6.1 Nordsieck Predictor—Corrector Method
12.6.2 Gear Predictor—Corrector Methods
12.7 Runge—Kutta Methods
12.7.1 Second Order Runge—Kutta Method
12.7.2 Third Order Runge—Kutta Method
12.7.3 Fourth Order Runge—Kutta Method
12.8 Quality Control and Adaptive Step Size Control
12.9 Extrapolation Methods
12.10 Linear Multistep Methods
12.10.1 Adams—Bashforth Methods
12.10.2 Adams—Moulton Methods
12.10.3 Backward Differentiation （Gear） Methods
12.10.4 Predictor—Corrector Methods
12.11 Verlet Methods
12.11.1 Liouville Equation
12.11.2 Split—Operator Approximation
12.11.3 Position Verlet Method
12.11.4 Velocity Verlet Method
12.11.5 Stormer—Verlet Method
12.11.6 Error Accumulation for the Stormer—Verlet Method
12.11.7 Beeman's Method
12.11.8 The Leapfrog Method
12.12 Problems
……
Part Ⅱ Simulation of Classical and Quantum Systems
Appendix Ⅰ Performing the Computer Experiments
Appendix Ⅱ Methods and Algorithms
References
Index
1 Error Analysis
1.1 Machine Numbers and Rounding Errors
1.2 Numerical Errors of Elementary Floating Point Operations
1.2.1 Numerical Extinction
1.2.2 Addition
1.2.3 Multiplication
1.3 Error Propagation
1.4 Stability of Iterative Algorithms
1.5 Example： Rotation
1.6 Truncation Error
1.7 Problems
2 Interpolation
2.1 Interpolating Functions
2.2 Polynomial Interpolation
2.2.1 Lagrange Polynomials
2.2.2 Barycentric Lagrange Interpolation
2.2.3 Newton's Divided Differences
2.2.4 Neville Method
2.2.5 Error of Polynomial Interpolation
2.3 Spline Interpolation
2.4 Rational Imerpolation
2.4.1 Pade Approximant
2.4.2 Barycentric Rational Interpolation
2.5 Multivariate Interpolation
2.6 Problems
3 Numerical Differentiahon
3.1 One—Sided Difference Quotient
3.2 Central Difference Quotient
3.3 Extrapolation Methods
3.4 Higher Derivatives
3.5 Partial Derivatives of Multivariate Functions
3.6 Problems
4 Numerical Integrahon
4.1 Equidistant Sample Points
4.1.1 Closed Newton—Cotes Formulae
4.1.2 Open Newton—Cotes Formulae
4.1.3 Composite Newton—Cotes Rules
4.1.4 Extrapolation Method （Romberg Integration）
4.2 Optimized Sample Points
4.2.1 Clenshaw—Curtis Expressions
4.2.2 Gaussian Integration
4.3 Problems
5 Systems of Inhomogeneous Linear Equations
5.1 Gaussian Elimination Method
5.1.1 Pivoting
5.1.2 Direct LU Decomposition
5.2 QR Decomposition
5.2.1 QR Decomposition by Orthogonalization
5.2.2 QR Decomposition hy Householder Reflections
5.3 Linear Equations wiih Tridiagonal Matrix
5.4 Cyclic Tridiagonal Systems
5.5 Iterative Solution of Inhomogeneous Linear Equations
5.5.1 General Relaxation Method
5.5.2 Jacobi Method
5.5.3 Gauss—Seidel Method
5.5.4 Damping and Successive Over—Relaxation
5.6 Conjugate Gradients
5.7 Matrix Inversion
5.8 Problems
6 Roots and Extremal Points
6.1 Root Finding
6.1.1 Bisection
6.1.2 Regula Falsi （False Position） Method
6.1.3 Newton—Raphson Method
6.1.4 Secant Method
6.1.5 Interpolation
6.1.6 Inverse Interpolation
6.1.7 Combined Methods
6.1.8 Multidimensional Root Finding
6.1.9 Quasi—Newton Methods
6.2 Function Minimization
6.2.1 TheTernary Search Method
6.2.2 The Golden Section Search Method （Brent's Method）
6.2.3 Minimization in Multidimensions
6.2.4 Steepest Descent Method
6.2.5 Conjugate Gradient Method
6.2.6 Newton—Raphson Method
6.2.7 Quasi—Newton Methods
6.3 Problems
Fourier Transformation
7.1 Fourier Integral and Fourier Series
7.2 Discrete Fourier Transformauon
7.2.1 Trigonometric Interpolation
7.2.2 Real Valued Functions
7.2.3 Approximate Continuous Fourier Transformation
7.3 Fourier Transform Algorithms
7.3.1 Goertzel's Algorithm
7.3.2 Fast Fourier Transformation
7.4 Problems
8 Random Numbers and Monte Carlo Methods
8.1 Some Basic Statistics
8.1.1 Probability Density and Cumulative Probability Distribution
8.1.2 Histogram
8.1.3 Expectation Values and Moments
8.1.4 Example： Fair Die
8.1.5 Normal Distribution
8.1.6 Multivariate Distributions
8.1.7 Central Limit Theorem
8.1.8 Example： Binomial Distribution
8.1.9 Average of Repeated Measurements
8.2 Random Numbers
8.2.1 Linear Congruent Mapping
8.2.2 Marsaglia—Zamann Method
8.2.3 Random Numbers with Given Distribution
8.2.4 Examples
8.3 Monte Carlo Integration
8.3.1 Numerical Calculation of π
8.3.2 Calculation of an Integral
8.3.3 More General Random Numbers
8.4 Monte Carlo Method for Thermodynamic Averages
8.4.1 Simple Sampling
8.4.2 Importance Sampling
8.4.3 Metropolis Algorithm
8.5 Problems
9 Eigenvalue Problems
9.1 Direct Solution
9.2 Jacobi Method
9.3 Tridiagonal Matrices
9.3.1 Characteristic Polynomial of a Tridiagonal Matrix
9.3.2 Special Tridiagonal Matrices
9.3.3 The QL Algorithm
9.4 Reduction to a Tridiagonal Matrix
9.5 Large Matrices
9.6 Problems
10 Data Fitting
10.1 LeastSquareFit
10.1.1 Linear Least Square Fit
10.1.2 Linear Least Square Fit with Orthogonalization
10.2 Singular Value Decomposition
10.2.1 Full Singular Value Decomposition
10.2.2 Reduced Singular Value Decomposition
10.2.3 Low Rank Matrix Approximation
10.2.4 Linear Least Square Fit with Singular Value Decomposition
10.3 Problems
11 Discretization of Differential Equations
11.1 Classification of Differential Equations
11.1.1 Linear Second Order PDE
11.1.2 Conservation Laws
11.2 Finite Differences
11.2.1 Finite Differences in Time
11.2.2 Stability Analysis
11.2.3 Method of Lines
11.2.4 Eigenvector Expansion
11.3 Finite Volumes
11.3.1 Discretization of fluxes
11.4 Weighted Residual Based Methods
11.4.1 Point Collocation Method
11.4.2 Sub—domain Method
11.4.3 Least Squares Method
11.4.4 Galerkin Method
11.5 Spectraland Pseudo—spectral Methods
11.5.1 Fourier Pseudo—spectral Methods
11.5.2 Example：Polynomial Approximation
11.6 Finite Elements
11.6.1 One—Dimensional Elements
11.6.2 Two—and Three—Dimensional Elements
11.6.3 One—Dimensional Galerkin FEM
11.7 Boundary Element Method
12 Equations of Motion
12.1 The State Vector
12.2 Time Evolution of the State Vector
12.3 Explicit Forward Euler Method
12.4 Implicit Backward Euler Method
12.5 Improved Euler Methods
12.6 Taylor Series Methods
12.6.1 Nordsieck Predictor—Corrector Method
12.6.2 Gear Predictor—Corrector Methods
12.7 Runge—Kutta Methods
12.7.1 Second Order Runge—Kutta Method
12.7.2 Third Order Runge—Kutta Method
12.7.3 Fourth Order Runge—Kutta Method
12.8 Quality Control and Adaptive Step Size Control
12.9 Extrapolation Methods
12.10 Linear Multistep Methods
12.10.1 Adams—Bashforth Methods
12.10.2 Adams—Moulton Methods
12.10.3 Backward Differentiation （Gear） Methods
12.10.4 Predictor—Corrector Methods
12.11 Verlet Methods
12.11.1 Liouville Equation
12.11.2 Split—Operator Approximation
12.11.3 Position Verlet Method
12.11.4 Velocity Verlet Method
12.11.5 Stormer—Verlet Method
12.11.6 Error Accumulation for the Stormer—Verlet Method
12.11.7 Beeman's Method
12.11.8 The Leapfrog Method
12.12 Problems
……
Part Ⅱ Simulation of Classical and Quantum Systems
Appendix Ⅰ Performing the Computer Experiments
Appendix Ⅱ Methods and Algorithms
References
Index
