Computational Physics

First published in 2007, this second edition describes the computational methods used in theoretical physics. New sections were added to cover finite element methods and lattice Boltzmann simulation, density functional theory, quantum molecular dynamics, Monte Carlo simulation, and diagonalisation of one-dimensional quantum systems. It covers many different areas of physics research and different computational methodologies, including computational methods such as Monte Carlo and molecular dynamics, various electronic structure methodologies, methods for solving partial differential equations, and lattice gauge theory. Throughout the book the relations between the methods used in different fields of physics are emphasised. Several new programs are described and can be downloaded from cambridge.org/9781107677135. The book requires a background in elementary programming, numerical analysis, and field theory, as well as undergraduate knowledge of condensed matter theory and statistical physics. It will be of interest to graduate students and researchers in theoretical, computational and experimental physics.

This new edition has been fully updated with several new sections and chapters. The book covers many different areas of physics research and different computational methodologies. Throughout the book the relations between the methods used in different fields of physics are emphasised. Several new programs are described and can be downloaded from cambridge.org/9780521833462. The book requires a background in elementary programming, numerical analysis, and field theory, and undergraduate knowledge on condensed matter theory and statistical physics. It will interest graduate students and researchers in theoretical, computational and experimental physics.

1. Introduction; 2. Quantum scattering with a spherically symmetric potential; 3. The variational method for the Schrödinger equation; 4. The Hartree-Fock method; 5. Density functional theory; 6. Solving the Schrödinger equation in periodic solids; 7. Classical equilibrium statistical mechanics; 8. Molecular dynamics simulations; 9. Quantum molecular dynamics; 10. The Monte Carlo method; 11. Transfer matrix and diagonalisation of spin chains; 12. Quantum Monte Carlo methods; 13. The infinite element method for partial differential equations; 14. The lattice Boltzmann method for fluid dynamics; 15. Computational methods for lattice field theories; 16. High performance computing and parallelism; Appendix A. Numerical methods; Appendix B. Random number generators; References; Index.

First published in 2007, this second edition is for graduate students and researchers in theoretical, computational and experimental physics.