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

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1 Introduction1

1.1 Computation and science1

1.2 The emergence of modern computers4

1.3 Computer algorithms and languages7

Exercises14

2 Approximation of a function16

2.1 Interpolation16

2.2 Least-squares approximation24

2.3 The Millikan experiment27

2.4 Spline approximation30

2.5 Random-number generators37

Exercises44

3 Numerical calculus49

3.1 Numerical differentiation49

3.2 Numerical integration56

3.3 Roots of an equation62

3.4 Extremes of a function66

3.5 Classical scattering70

Exercises76

4 Ordinary differential equations80

4.1 Initial-value problems81

4.2 The Euler and Picard methods81

4.3 Predictor-corrector methods83

4.4 The Runge-Kutta method88

4.5 Chaotic dynamics of a driven pendulum90

4.6 Boundary-value and eigenvalue problems94

4.7 The shooting method96

4.8 Linear equations and the Sturm-Liouville problem99

4.9 The one-dimensional Schrodinger equation105

Exercises115

5 Numerical methods for matrices119

5.1 Matrices in physics119

5.2 Basic matrix operations123

5.3 Linear equation systems125

5.4 Zeros and extremes of multivariable functions133

5.5 Eigenvalue problems138

5.6 The Faddeev-Leverrier method147

5.7 Complex zeros of a polynomial149

5.8 Electronic structures of atoms153

5.9 The Lanczos algorithm and the many-body problem156

5.10 Random matrices158

Exercises160

6 Spectral analysis164

6.1 Fourier analysis and orthogonal functions165

6.2 Discrete Fourier transform166

6.3 Fast Fourier transform169

6.4 Power spectrum of a driven pendulum173

6.5 Fourier transform in higher dimensions174

6.6 Wavelet analysis175

6.7 Discrete wavelet transform180

6.8 Special functions187

6.9 Gaussian quadratures191

Exercises193

7 Partial differential equations197

7.1 Partial differential equations in physics197

7.2 Separation of variables198

7.3 Discretization of the equation204

7.4 The matrix method for difference equations206

7.5 The relaxation method209

7.6 Groundwater dynamics213

7.7 Initial-value problems216

7.8 Temperature field of a nuclear waste rod219

Exercises222

8 Molecular dynamics simulations226

8.1 General behavior of a classical system226

8.2 Basic methods for many-body systems228

8.3 The Verlet algorithm232

8.4 Structure of atomic clusters236

8.5 The Gear predictor-corrector method239

8.6 Constant pressure，temperature，and bond length241

8.7 Structure and dynamics of real materials246

8.8 Ab initio molecular dynamics250

Exercises254

9 Modeling continuous systems256

9.1 Hydrodynamic equations256

9.2 The basic finite element method258

9.3 The Ritz variational method262

9.4 Higher-dimensional systems266

9.5 The finite element method for nonlinear equations269

9.6 The particle-in-cell method271

9.7 Hydrodynamics and magnetohydrodynamics276

9.8 The lattice Boltzmann method279

Exercises282

10 Monte Carlo simulations285

10.1 Sampling and integration285

10.2 The Metropolis algorithm287

10.3 Applications in statistical physics292

10.4 Critical slowing down and block algorithms297

10.5 Variational quantum Monte Carlo simulations299

10.6 Green’s function Monte Carlo simulations303

10.7 Two-dimensional electron gas307

10.8 Path-integral Monte Carlo simulations313

10.9 Quantum lattice models315

Exercises320

11 Genetic algorithm and programming323

11.1 Basic elements of a genetic algorithm324

11.2 The Thomson problem332

11.3 Continuous genetic algorithm335

11.4 Other applications338

11.5 Genetic programming342

Exercises345

12 Numerical renormalization347

12.1 The scaling concept347

12.2 Renormalization transform350

12.3 Critical phenomena：the Ising model352

12.4 Renormalization with Monte Carlo simulation355

12.5 Crossover：the Kondo problem357

12.6 Quantum lattice renormalization360

12.7 Density matrix renormalization364

Exercises367

References369

Index381