计算物理学导论 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

计算物理学导论 英文版PDF格式电子书版下载

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1 Introduction1

1.1 Computation and science1

1.2 The emergence of modern computers2

1.3 Computer algorithms and languages4

2 Basic numerical methods11

2.1 Interpolations and approximations11

2.2 Differentiation and integration25

2.3 Zeros and extremes of a single-variable function31

2.4 Classical scattering39

2.5 Random number generators45

3 Ordinary differential equations55

3.1 Initial-value problems56

3.2 The Euler and Picard methods56

3.3 Predictor-corrector methods58

3.4 The Runge-Kutta method60

3.5 Chaotic dynamics of a driven pendulum63

3.6 Boundary-value and eigenvalue problems67

3.7 The shooting method69

3.8 Linear equations and the Sturm-Liouville problem74

3.9 The one-dimensional Schrodinger equation79

4 Numerical methods for matrices88

4.1 Matrices in physics88

4.2 Basic matrix operations91

4.3 Linear equation systems93

4.4 Zeros and extremes of a multivariable function103

4.5 Eigenvalue problems107

4.6 The Faddeev-Leverrier method116

4.7 Electronic structure of atoms117

4.8 The Lanczos algorithm and the many-body problem120

4.9 Random matrices122

5 Spectral analysis and Gaussian quadrature127

5.1 The Fourier transform and orthogonal functions128

5.2 The discrete Fourier transform129

5.3 The fast Fourier transform132

5.4 The power spectrum of a driven pendulum137

5.5 The Fourier transform in higher dimensions139

5.6 Wavelet analysis140

5.7 Special functions148

5.8 Gaussian quadrature153

6 Partial differential equations158

6.1 Partial differential equations in physics158

6.2 Separation of variables159

6.3 Discretization of the equation163

6.4 The matrix method for difference equations165

6.5 The relaxation method170

6.6 Groundwater dynamics173

6.7 Initial-value problems178

6.8 Temperature field of nuclear waste storage facilities181

7 Molecular dynamics simulations186

7.1 General behavior of a classical system186

7.2 Basic methods for many-body systems188

7.3 The Verlet algorithm192

7.4 Structure of atomic clusters197

7.5 The Gear predictor-corrector method200

7.6 Constant pressure， temperature， and bond length202

7.7 Structure and dynamics of real materials208

7.8 Ab initio molecular dynamics212

8 Modeling continuous systems219

8.1 Hydrodynamic equations219

8.2 The basic finite element method221

8.3 The Ritz variational method226

8.4 Higher-dimensional systems230

8.5 The finite element method for nonlinear equations234

8.6 The particle-in-cell method236

8.7 Hydrodynamics and magnetohydrodynamics241

8.8 The Boltzmann lattice-gas method244

9 Monte Carlo simulations250

9.1 Sampling and integration250

9.2 The Metropolis algorithm253

9.3 Applications in statistical physics260

9.4 Critical slowing down and block algorithms265

9.5 Variational quantum Monte Carlo simulations267

9.6 Green’s function Monte Carlo simulations272

9.7 Path-integral Monte Carlo simulations276

9.8 Quantum lattice models278

10 Numerical renormalization286

10.1 The scaling concept286

10.2 Renormalization transform289

10.3 Critical phenomena： The Ising model291

10.4 Renormalization with Monte Carlo simulation295

10.5 Crossover： The Kondo problem296

10.6 Quantum lattice renormalization300

10.7 Density matrix renormalization304

11 Symbolic computing309

11.1 Symbolic computing systems309

11.2 Basic symbolic mathematics311

11.3 Computer calculus313

11.4 Linear systems315

11.5 Nonlinear systems318

11.6 Differential equations320

11.7 Computer graphics324

11.8 Dynamics of a flying sphere326

12 High-performance computing332

12.1 The basic concept332

12.2 High-performance computing systems334

12.3 Parallelism and parallel computing337

12.4 Data parallel programming341

12.5 Distributed computing and message passing349

12.6 Some current applications354

References357

Index367