## Computational Physics: Fortran VersionComputational 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 (Please follow the link at the bottom of the page). 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. |

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### Contents

1 | |

20 | |

55 | |

Chapter 4 Special Functions and Gaussian Quadrature | 85 |

Matrix Operations | 109 |

Chapter 6s Elliptic Partial Differential Equations | 145 |

Parabolic Partial Differential Equations | 169 |

Monte Carlo Methods | 197 |

How to use the programs | 231 |

Programs for the Examples | 243 |

Programs for the Projects | 409 |

Common Utility Codes | 567 |

Appendix E Network File Transfer | 621 |

Index 681 | 631 |

### Common terms and phrases

algorithm approximation array boundary conditions calculate CALL CLEAR cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc C Global central potential COMPUTATIONAL PHYSICS constant CONTINUE contour default value derivative DESCRP DEVICE EQ dimensions display header screen eigenvalue eigenvectors electron END cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc SUBROUTINE energy evaluate field values FORMAT FORMAT FORMAT FORTRAN Gaussian GFILE Global variables GOTO graphics output graphing hardcopy Hartree-Fock INCLUDE 10.ALL INCLUDE GRFDAT.ALL INCLUDE MENU.ALL Input variables INTEGER INTEGER FILE INTEGER MUNIT INTEGER NLINES INTEGER PAPER INTEGER SCREEN IPLOT iteration KBIG lattice points Lennard-Jones potential matrix menu method MINTS momentum Monte Carlo MPRMPT MUNIT EQ number of lines OUNIT PARAM partial wave particle Passed variables physical plot potential problem quadrature radial radius random number REAL recursion RETURN END cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc scaled scattering scattering amplitude Schroedinger equation solution solve step stream function string sublattice surface of section terminal INTEGER text output TFILE trajectory TTERM turning points wave function WRITE MUNIT zero

### Popular passages

Page 208 - Gaussian-distributed random numbers is based on the central limit theorem, which states that the sum of a large number of independent random variables is Gaussian.

Page 100 - Another immediate consequence of unitarity is the optical theorem, which relates the total cross section to the imaginary part of the forward scattering amplitude.

Page 127 - ... surface thickness', the distance over which the density drops from 90% to 10% of its maximum value.

Page 75 - The kinetic energy is the sum of the kinetic energies of the...

Page 55 - Jacobi equation for a particle of mass m and energy E moving in a potential V(r), The preceding mechanics considerations can thus be translated into optics equivalents.13 Of course, phase <|>(r) is dimensionless, whereas W(r) has the dimensions of "action.

Page 69 - V0v(x), where the dimensionless function v(x) has a minimum value of —1 and a maximum value of +1.

Page 22 - The factor of 2 in front of the integral accounts for the fact that there are two active force producing surfaces in this particular machine.

Page 190 - Setting all derivatives to zero yields a set of algebraic equations that can be solved for the equilibrium point.

Page 215 - This mimics the spin-1/2 situation, although note that we take the spins to be classical degrees of freedom and do not impose the angular momentum commutation rules characteristic of a quantum description.