| Description |
1 online resource (656 pages) |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Preface; Preface to the FORTRAN Edition; How to use this book; Table of Contents; Chapter 1: Basic Mathematical Operations; 1.1 Numerical differentiation; 1.2 Numerical quadrature; 1.3 Finding roots; 1.4 Semiclassical quantization of molecular vibrations; Project I: Scattering by a central potential; Chapter 2: Ordinary Differential Equations; 2.1 Simple methods; 2.2 Multistep and implicit methods; 2.3 Runge-Kutta methods; 2.4 Stability; 2.5 Order and chaos in two-dimensional motion; Project II: The structure of white dwarf stars |
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II. 1 The equations of equilibriumII. 2 The equation of state; II. 3 Scaling the equations; II. 4 Solving the equations; Chapter 3: Boundary Value and Eigenvalue Problems; 3.1 The Numerov algorithm; 3.2 Direct integration of boundary value problems; 3.3 Greenâ#x80;#x99;s function solution of boundary value problems; 3.4 Eigenvalues of the wave equation; 3.5 Stationary solutions of the one-dimensional Schroedinger equation; Project III: Atomic structure in the Hartree-Fock approximation; III. 1 Basis of the Hartree-Fock approximation; III. 2 The two-electron problem; III. 3 Many-electron systems |
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III. 4 Solving the equationsChapter 4: Special Functions and Gaussian Quadrature; 4.1 Special functions; 4.2 Gaussian quadrature; 4.3 Born and eikonal approximations to quantum scattering; Project IV: Partial wave solution of quantum scattering; IV. 1 Partial wave decomposition of the wave function; IV. 2 Finding the phase shifts; IV. 3 Solving the equations; Chapter 5: Matrix Operations; 5.1 Matrix inversion; 5.2 Eigenvalues of a tri-diagonal matrix; 5.3 Reduction to tri-diagonal form; 5.4 Determining nuclear charge densities; Project V: A schematic shell model; V.1 Definition of the model |
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V.2 The exact eigenstatesV. 3 Approximate eigenstates; V.4 Solving the model; Chapter 6: Elliptic Partial Differential Equations; 6.1 Discretization and the variational principle; 6.2 An iterative method for boundary value problems; 6.3 More on discretization; 6.4 Elliptic equations in two dimensions; Project VI: Steady-state hydrodynamics in two dimensions; VI. 1 The equations and their discretization; VI. 2 Boundary conditions; VI. 3 Solving the equations; Chapter 7: Parabolic Partial Differential Equations; 7.1 Naive discretization and instabilities |
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7.2 Implicit schemes and the inversion of tri-diagonal matrices7.3 Diffusion and boundary value problems in two dimensions; 7.4 Iterative methods for eigenvalue problems; 7.5 The time-dependent Schroedinger equation; Project VII: Self-organization in chemical reactions; VII. 1 Description of the model; VII. 2 Linear stability analysis; VII. 3 Numerical solution of the model; Chapter 8: Monte Carlo Methods; 8.1 The basic Monte Carlo strategy; 8.2 Generating random variables with a specified distribution; 8.3 The algorithm of Metropolis et al., ; 8.4 The Ising model in two dimensions |
| Summary |
Computational Physics is designed to provide direct experience in the computer modeling of physical systems. Its scope includes the essential numerical techniques needed to "do physics" on a computer. Each of these is developed heuristically in the text, with the aid of simple mathematical illustrations. However, the real value of the book is in the eight Examples and Projects, where the reader is guided in applying these techniques to substantial problems in classical, quantum, or statistical mechanics. These problems have been chosen to enrich the standard physics curriculum at the advanced undergraduate or beginning graduate level. The book will also be useful to physicists, engineers, and chemists interested in computer modeling and numerical techniques. Although the user-friendly and fully documented programs are written in FORTRAN, a casual familiarity with any other high-level language, such as BASIC, PASCAL, or C, is sufficient. The codes in BASIC and FORTRAN are available on the web at http://www.computationalphysics.info. They are available in zip format, which can be expanded on UNIX, Window, and Mac systems with the proper software. The codes are suitable for use (with minor changes) on any machine with a FORTRAN-77 compatible compiler or BASIC compiler. The FORTRAN graphics codes are available as well. However, as they were originally written to run on the VAX, major modifications must be made to make them run on other machines |
| Notes |
Project VIII: Quantum Monte Carlo for the H2 molecule |
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Print version record |
| Subject |
Numerical analysis.
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Physics -- Computer programs
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Mathematical physics -- Data processing
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Differential equations -- Numerical solutions.
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FORTRAN (Computer program language)
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Mathematical physics.
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Differential equations -- Numerical solutions
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FORTRAN (Computer program language)
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Mathematical physics
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Mathematical physics -- Data processing
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Numerical analysis
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Physics -- Computer programs
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| Form |
Electronic book
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| ISBN |
9780429962578 |
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0429962576 |
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