Computational Physics

This book presents basic and advanced computational physics. It contains well-presented and simple mathematical descriptions of key algorithms. Includes exercises and solutions to all topics, as well as computer experiments.

This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics.

The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods.

The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into notonly the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments.

Features numerous computer examples; no programming skills necessary Includes separate parts on numerical methods and simulations Gives detailed explanations without mathematical proofs Covers many basic areas in physics Discusses standard numerical methods and more recent developments Contains exercises and solutions to all topics Includes supplementary material: sn.pub/extras

Autorentext

Prof. Scherer received his PhD in experimental and theoretical physics in 1984. He joined the National Institute of Advanced Industrial Science and Technology (AIST) in Tsukuba, Japan, as a visiting scientist in 2001 and 2003. His area of research includes biomolecular physics and the computer simulation of molecular systems with classical and quantum methods. He has published books on theoretical molecular physics and computational physics.

Inhalt
Part I Numerical Methods.- Error Analysis.- Interpolation.- Numerical Differentiation.- Numerical Integration.- Systems of Inhomogeneous Linear Equations.- Roots and Extremal Points.- Fourier Transformation.- Random Numbers and Monte-Carlo Methods.- Eigenvalue Problems.- Data Fitting.- Discretization of Differential Equations.- Equations of Motion.- Part II Simulation of Classical and Quantum Systems.- Rotational Motion.- Molecular Dynamics.- Thermodynamic Systems.- Random Walk and Brownian Motion.- Electrostatics.- Waves.- Diffusion.- Nonlinear Systems.- Simple Quantum Systems.