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 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 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