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 statisticalphysics
　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-particlemethod
　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
8　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 hydrogenmolecule
　9.4 orthonormalisation; conjugate gradient and rm-diistechniques
　9.5 implementation of the car-parrinello technique forpseudopotential 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 differentialequations
　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-randomnumbers
　B3 nonuniform random number generators
　exercises
　references
　index