计算物理学 : 第2版

preface to the first edition

preface to the second edition

1 introduction

1.1 physics and computational physics

1.2 classical mechanics and statistical mechanics

1.3 stochastic simulations

1.4 electrodynamics and hydrodynamics

1.5 quantum mechanics

1.6 relations between quantum mechanics and classical statistical physics

1.7 quantum molecular dynamics

1.8 quantum field theory

1.9 about this book

exercises

references

2 quantum scattering with a spherically symmetric

potential

2.1 introduction

2.2 a program for calculating cross sections

2.3 calculation of scattering cross sections

exercises

references

3 the variational method for the schr'odinger equation

3.1 variational calculus

3.2 examples of variational calculations

3.3 solution of the generalised eigenvalue problem

3.4 perturbation theory and variational calculus

exercises

references

4 the hartree-fock method

4.1 introduction

4.2 the bom-oppenheimer approximation and the independent-particle method

4.3 the helium atom

4.4 many-electron systems and the slater determinant

4.5 self-consistency and exchange: hartree-fock theory

4.6 basis functions

4.7 the structure of a hartree-fock computer program

4.8 integrals involving gaussian functions

4.9 applications and results

4.10 improving upon the hartree-fock approximation

exercises

references

5 density functional theory

5.1 introduction

5.2 the local density approximation

5.3 exchange and correlation: a closer look

5.4 beyond dft: one- and two-particle excitations

5.5 a density functional program for the helium atom

5.6 applications and results

exercises

references

6 solving the schriodinger equation in periodic solids

6.1 introduction: definitions

6.2 band structures and bloch's theorem

6.3 approximations

6.4 band structure methods and basis functions

6.5 augmented plane wave'methods

6.6 the linearised apw （lapw） method

6.7 the pseudopotential method

6.8 extracting information from band structures

6.9 some additional remarks

6.10 other band methods

exercises

references

7 classical equilibrium statistical mechanics

7.1 basic theory

7.2 examples of statistical models; phase transitions

7.3 phase transitions

7.4 determination of averages in simulations

exercises

references

molecular dynamics simulations

8.1 introduction

8.2 molecular dynamics at constant energy

8.3 a molecular dynamics simulation program for argon

8.4 integration methods: symplectic integrators

8.5 molecular dynamics methods for different ensembles

8.6 molecular systems

8.7 long-range interactions

8.8 langevin dynamics simulation

8.9 dynamical quantities: nonequilibrium molecular dynamics

exercises

references

9 quantum molecular dynamics

9.1 introduction

9.2 the molecular dynamics method

9.3 an example: quantum molecular dynamics for the hydrogen molecule

9.4 orthonormalisation; conjugate gradient and rm-diis techniques

9.5 implementation of the car-parrinello technique for pseudopotential dft

exercises

references

10 the monte carlo method

10.1 introduction

10.2 monte carlo integration

10.3 importance sampling through markov chains

10.4 other ensembles

10.5 estimation of free energy and chemical potential

10.6 further applications and monte carlo methods

10.7 the temperature of a finite system

exercises

references

11 transfer matrix and diagonalisation of spin chains

11.1 introduction

11.2 the one-dimensional ising model and the transfer matrix

11.3 two-dimensional spin models

11.4 more complicated models

11.5 'exact' diagonalisation of quantum chains

11.6 quantum renormalisation in real space

11.7 the density matrix renormalisation group method

exercises

references

12 quantum monte carlo methods

12.1 introduction

12.2 the variational monte carlo method

12.3 diffusion monte carlo

12.4 path-integral monte carlo

12.5 quantum monte carlo on a lattice

12.6 the monte carlo transfer matrix method

exercises

references

13 the finite element method for partial differential equations

13.1 introduction

13.2 the poisson equation

13.3 linear elasticity

13.4 error estimators

13.5 local refinement

13.6 dynamical finite element method

13.7 concurrent coupling of length scales: fem and md

exercises

references

14 the lattice boltzmann method for fluid dynamics

14.1 introduction

14.2 derivation of the navier-stokes equations

14.3 the lattice boltzmann model

14.4 additional remarks

14.5 derivation of the navier-stokes equation from the

lattice boltzmann model

exercises

references

15 computational methods for lattice field theories

15.1 introduction

15.2 quantum field theory

15.3 interacting fields and renormalisation

15.4 algorithms for lattice field theories

15.5 reducing critical slowing down

15.6 comparison of algorithms for scalar field theory

15.7 gauge field theories

exercises

references

16 high performance computing and parallelism

16.1 introduction

16.2 pipelining

16.3 parallelism

16.4 parallel algorithms for molecular dynamics

references

appendix a numerical methods

a1 about numerical methods

a2 iterative procedures for special functions

a3 finding the root of a function

a4 finding the optimum of a function

a5 discretisation

a6 numerical quadratures

a7 differential equations

a8 linear algebra problems

a9 the fast fourier transform

exercises

references

appendix b random number generators

b1 random numbers and pseudo-random numbers

b2 random number generators and properties of pseudo-random numbers

b3 nonuniform random number generators

exercises

references

index

《计算物理学（第2版）》是一部理论物理研究的计算方法的教程。这是第二版，在第一版的基础上做了大量的更新，内容更加全面。新增加的部分包括，有限元方法，格点boltzmann模拟，密度函数理论，量子分子动力学，monte carlo模拟和一维量子系统的对角化。书中囊括了了物理研究的很多不同方面和不同计算方法论。如monte carlo方法和分子模拟动力学以及各种电子结构方法论，偏微分方程解方法，格点规范理论。全书都在强调不同物理场中的方法之间的关系，内容较为简洁明快，具有基本编程，数值分析，场论以及凝聚态理论和统计物理的本科知识背景就可以完全读懂《计算物理学（第2版）》。不管是理论物理，计算物理还是实验物理专业的研究生还是科研人员，《计算物理学（第2版）》都相当有参考价值。目次：导论；具有球对称势的量子散射；schrdinger方程的变分大法；hartree-fock方法；密度函数理论；周期性固态schr.dinger方程解法；经典平衡态统计力学；分子动力学模拟；量子分子动力学；monte carlo方法；变换矩阵和自旋链的对角化；量子monte carlo方法，偏微分方程的有限元方法，流体力学的lattice boltzmann方法，格点场论的计算方法；高效能计算和并行法；附：数值法；随机数发生器。
读者对象：物理专业，包括理论物理，计算物理，实验物理的高年级本科生，研究生和相关的科研人员。