计算物理学 原书第2版 英文版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

计算物理学 原书第2版 英文版PDF格式电子书版下载

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1 Introduction1

1.1 Physics and computational physics1

1.2 Classical mechanics and statistical mechanics1

1.3 Stochastic simulations4

1.4 Electrodynamics and hydrodynamics5

1.5 Quantum mechanics6

1.6 Relations between quantum mechanics and classical statistical physics7

1.7 Quantum molecular dynamics8

1.8 Quantum field theory9

1.9 About this book9

Exercises11

References13

2 Quantum scattering with a spherically symmetric potential14

2.1 Introduction14

2.2 A program for calculating cross sections18

2.3 Calculation of scattering cross sections25

Exercises27

References28

3 The variational method for the Schr？dinger equation29

3.1 Variational calculus29

3.2 Examples of variational calculations32

3.3 Solution of the generalised eigenvalue problem36

3.4 Perturbation theory and variational calculus37

Exercises39

References41

4 The Hartree-Fock method43

4.1 Introduction43

4.2 The Born-Oppenheimer approximation and the independent-particle method44

4.3 The helium atom46

4.4 Many-electron systems and the Slater determinant52

4.5 Self-consistency and exchange：Hartree-Fock theory54

4.6 Basis functions60

4.7 The structure of a Hartree-Fock computer program69

4.8 Integrals involving Gaussian functions73

4.9 Applications and results77

4.10 Improving upon the Hartree-Fock approximation78

Exercises80

References87

5 Density functional theory89

5.1 Introduction89

5.2 The local density approximation95

5.3 Exchange and correlation：a closer look97

5.4 Beyond DFT：one- and two-particle excitations101

5.5 A density functional program for the helium atom109

5.6 Applications and results114

Exercises116

References119

6 Solving the Schr？dinger equation in periodic solids122

6.1 Introduction：definitions123

6.2 Band structures and Bloch’s theorem124

6.3 Approximations126

6.4 Band structure methods and basis functions133

6.5 Augmented plane wave methods135

6.6 The linearised APW（LAPW）method141

6.7 The pseudopotential method144

6.8 Extracting information from band structures160

6.9 Some additional remarks162

6.10 Other band methods163

Exercises163

References167

7 Classical equilibrium statistical mechanics169

7.1 Basic theory169

7.2 Examples of statistical models;phase transitions176

7.3 Phase transitions184

7.4 Determination of averages in simulations192

Exercises194

References195

8 Molecular dynamics simulations197

8.1 Introduction197

8.2 Molecular dynamics at constant energy200

8.3 A molecular dynamics simulation program for argon208

8.4 Integration methods：symplectic integrators211

8.5 Molecular dynamics methods for different ensembles223

8.6 Molecular systems232

8.7 Long-range interactions241

8.8 Langevin dynamics simulation247

8.9 Dynamical quantities：nonequilibrium molecular dynamics251

Exercises253

References259

9 Quantum molecular dynamics263

9.1 Introduction263

9.2 The molecular dynamics method266

9.3 An example：quantum molecular dynamics for the hydrogen molecule272

9.4 Orthonormalisation;conjugate gradient and RM-DIIS techniques278

9.5 Implementation of the Car-Parrinello technique for pseudopotential DFT289

Exercises290

References293

10 The Monte Carlo method295

10.1 Introduction295

10.2 Monte Carlo integration296

10.3 Importance sampling through Markov chains299

10.4 Other ensembles310

10.5 Estimation of free energy and chemical potential316

10.6 Further applications and Monte Carlo methods319

10.7 The temperature of a finite system330

Exercises334

References335

11 Transfer matrix and diagonalisation of spin chains338

11.1 Introduction338

11.2 The one-dimensional Ising model and the transfer matrix339

11.3 Two-dimensional spin models343

11.4 More complicated models347

11.5 ’Exact’diagonalisation of quantum chains349

11.6 Quantum renormalisation in real space355

11.7 The density matrix renormalisation group method358

Exercises365

References370

12 Quantum Monte Carlo methods372

12.1 Introduction372

12.2 The variational Monte Carlo method373

12.3 Diffusion Monte Carlo387

12.4 Path-integral Monte Carlo398

12.5 Quantum Monte Carlo on a lattice410

12.6 The Monte Carlo transfer matrix method414

Exercises417

References421

13 The finite element method for partial differential equations423

13.1 Introduction423

13.2 The Poisson equation424

13.3 Linear elasticity429

13.4 Error estimators434

13.5 Local refinement436

13.6 Dynamical finite element method439

13.7 Concurrent coupling of length scales：FEM and MD440

Exercises445

References446

14 The lattice Boltzmann method for fluid dynamics448

14.1 Introduction448

14.2 Derivation of the Navier-Stokes equations449

14.3 The lattice Boltzmann model455

14.4 Additional remarks458

14.5 Derivation of the Navier-Stokes equation from the lattice Boltzmann model460

Exercises463

References464

15 Computational methods for lattice field theories466

15.1 Introduction466

15.2 Quantum field theory467

15.3 Interacting fields and renormalisation473

15.4 Algorithms for lattice field theories477

15.5 Reducing critical slowing down491

15.6 Comparison of algorithms for scalar field theory509

15.7 Gauge field theories510

Exercises532

References536

16 High performance computing and parallelism540

16.1 Introduction540

16.2 Pipelining541

16.3 Parallelism545

16.4 Parallel algorithms for molecular dynamics552

References556

Appendix A Numerical methods557

A1 About numerical methods557

A2 Iterative procedures for special functions558

A3 Finding the root of a function559

A4 Finding the optimum of a function560

A5 Discretisation565

A6 Numerical quadratures566

A7 Differential equations568

A8 Linear algebra problems590

A9 The fast Fourier transform598

Exercises601

References603

Appendix B Random number generators605

B1 Random numbers and pseudo-random numbers605

B2 Random number generators and properties of pseudo-random numbers606

B3 Nonuniform random number generators609

Exercises611

References612

Index613