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Koonin S.E., Meredith D.C. — Computational Physics-Fortran Version
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Название: Computational Physics-Fortran VersionАвторы: Koonin S.E., Meredith D.C. Аннотация: 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.
Язык: Рубрика: Руководства по программному обеспечению /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 639Добавлена в каталог: 24.11.2013Операции: Положить на полку |
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83 17 19 221ff 224 221 230 223 224 17 72 133 221 40 Eri B 53 6-12 potential 14 222 see Abscissae, gaussian quadrature 95 Acceleration parameter, elliptic partial differential equations 180 Accuracy monitoring, ordinary differential equations 32 Accuracy, ordinary differential equations 68 Accuracy, partial differential equation 174 Accuracy, quadrature 8 9 action 16 Adams — Bashforth, four-step method 30 Adams — Bashforth, two-step method 29 Adams — Moulton methods 31 Alternating-direction methods, partial differential equation 180 Angle, scattering 20 Annihilation operator 135 Anti-ferromagnetic couplings 220 Anti-ferromagnetism 216 Approximation, Born 96ff 121 Approximation, Born — Oppenheimer 14 221 Approximation, central-field 78 Approximation, eikonal 96ff 99 129 Approximation, filling 78 Approximation, Hartree — Fock 72ff 222 Approximation, linear 109 123 Approximation, self-consistent field 72 Approximation, semiclassical 14 98 139 Approximation, WKB 16 Atomic, nucleus 120 Atomic, orbitals, linear combination 224 Atomic, Structure 72ff Atoms, low-energy resonances 108 Atoms, multi-electron 72 Auto-correlation, Metropolis algorithm 214 219 Bessel function, cylindrical 67 87 Bessel function, cylindrical, polynomial approximation 87 Bessel function, cylindrical, recursion relation 81ff Bessel function, spherical 92 104 Binary alloy 215 Bode's rule 9 Born approximation 96ff 121 Born scattering amplitude 98 Born — Oppenheimer approximation 14 221 Bound solutions 14 67 Boundary conditions, Dirichlet 146 169 Boundary conditions, fixed 190 Boundary conditions, mixed 146 Boundary conditions, Neumann 146 150 178 Boundary conditions, no-flux 190 Boundary conditions, no-slip 165 Boundary conditions, periodic 158 Boundary value problems 55ff Boundary value problems, Green's function solution 61ff Boundary value problems, round-off error 60 Boundary value problems, shooting method 64 67 Brusselator 189ff Brusselator, equilibrium values 190 Brusselator, linear stability analysis 191ff canonical ensemble 216 Canonical transformation 45 Capacitance 157 Central potential 20 38 45 103 Central-field approximation 78 Centrifugal potential 21 104 Chandrasekhar mass 53 Chaotic, dynamics 37ff. Chaotic, regions of phase space 42 Charge density parameters, uncertainty 125 Chemical reactions 189ff Chi-square, minimization 123 Classical scattering 20ff Classically forbidden region 67 codes see "Programs" Collective behavior 134 Constant of the motion 38 Continuity equation 159 Convection 159 Convergence, root finding 13 Correlation, electrons in 224 Correlation, Metropolis algorithm 214 219 Coulomb potential 14 57 72 121 Cowling's method 56 Creation operator 135 Cross section, differential 20 121 Cross section, Mott 122 Cross section, Rutherford 121 Cross section, total 97 Cylindrical Bessel function 67 87ff Cylindrical geometry, elliptic partial differential equations 156 Data analysis 123 de Broglie wave number 16 Deflection function 20ff Degeneracy pressure, electrons 46 Determinant, matrix 110 112 Diatomic molecule 14 dielectric constant 155 Differential cross section 20 121 Differential equations, ordinary 25ff Differential equations, partial 145ff Differentiation 1 2ff Differentiation, 2-point 3 Differentiation, 3-point 3 Differentiation, 4-point 6 Differentiation, 5-point 5 6 Differentiation, backward 3 Differentiation, forward 3 Differentiation, instability 4 Differentiation, round-off error 4 Differentiation, symmetric 3 Diffusion coefficient 155 Diffusion equation 146 Dirac scattering 129 Dirichlet boundary conditions 146 169 Double-well potential 72 Drift function, Path Integral Monte Carlo 226 Driving term, ordinary differential equation 55 Eddy 167 Eigenvalue problem, differential equation 56 64ff 147 Eigenvalue problem, differential equation, iterative method 188ff Eigenvalue problem, differential equation, iterative method, round-off errors 186 Eigenvalue problem, differential equation, non-linear 72 Eigenvalue problem, differential equation, root finding 65 Eigenvalue problem, matrix 112ff Eigenvalue problem, matrix, Gerschgorin's bounds 114 Eigenvalue problem, matrix, Lanczos algorithm 119 Eigenvalue problem, matrix, root finding 113 Eigenvalue problem, matrix, tri-diagonal matrix 113 Eigenvectors, inverse iteration 118 Eikonal, approximation 96ff 99 129 Eikonal, scattering amplitude 99 Electronic eigenvalue, 221 Electrons, correlation, 224 Electrons, degeneracy pressure in white dwarf stars 46 Electrons, density in atoms 74 Electrons, free Fermi gas 47 Electrons, gas 221 Electrons, scattering from neutral atoms, high-energy 96ff Electrons, scattering from neutral atoms, low-energy 103ff Electrons, scattering from nuclei 120ff Electrons, spin state in atoms 73 Electrons, valence 78 Electrostatics problem 157 Elliptic fixed points 42 Elliptic partial differential equations 145ff Elliptic partial differential equations, cylindrical geometry 156 Elliptic partial differential equations, eigenvalue problem 147 181ff Elliptic partial differential equations, iterative methods 151ff Elliptic partial differential equations, spatially varying dielectric constant 155 Elliptic partial differential equations, spherical geometry 156 Elliptic partial differential equations, two-dimensional 180 Elliptic partial differential equations, variational principle 147ff Equation of state 47 Equation of state, polytropic 52 Equilibrium values, Brusselator 190 Errors see also "Accuracy" "Inaccuracy" "Instability" "Round-off" "Stability" "Uncertainty" Errors, Monte Carlo methods 204 Euler — Lagrange equations 75 Euler's method 26 Exchange, energy 79 Exchange, matrix elements 75 Explicit scheme, parabolic partial differential equation 170 Faraday Cage 157 Fermi, function 126 Fermi, gas of electrons 47 Fermi, momentum 48 Ferromagnetic couplings 220 ferromagnetism 215 Filling approximation 78 Finding of roots 11ff see Finite square-well potential 72 Fixed boundary condition 190 Fixed points 42 Fixed points, elliptic 42 Fixed points, hyperbolic 42 Fluid flow 158ff Fluid flow, incompressible, viscous 159 Fluid flow, jump geometry 168 Fluid flow, nozzle geometry 168 Fock potential 80 Forbidden region, classical 67 Force, gravitational 46 Force, pressure 159 Force, viscous 159 167 Fourier expansion 126 127 Fourier — Bessel transform 129 Gauss — Chebyshev quadrature 96 Gauss — Hermite quadrature 95 Gauss — Jordan method, matrix inversion 110 Gauss — Laguerre quadrature 94 Gauss — Legendre quadrature 94 102 Gauss — Seidel iteration 151 Gaussian, distribution, random number generation 208 Gaussian, elimination and back-substitution 175 Gaussian, quadrature 85ff 92ff Gaussian, wavepacket 188 Gaussian, well potential 101 188 Geometry, cylindrical, elliptic partial differential equations 156 Geometry, jump, fluid flow 168 Geometry, nozzle, fluid flow 168 Geometry, spherical, elliptic partial differential equations 156 Gerschgorin's bounds, eigenvalue problem 114 Gravitational force 46 Green's function, Monte Carlo 225 Green's function, solution, boundary value problems 61ff Hamiltonian, integrable 38 Hamiltonian, separable 38 Harmonic-oscillator potential, path integral Monte Carlo 230 Hartree — Fock approximation 72ff 133 HD molecule 17 He atom 230 Heat bath algorithm, Monte Carlo methods 220 Heisenberg model 215 Henon and Heiles potential 42 Hermite polynomials 87 High energy quantum scattering 96ff High energy quantum scattering, Born approximation 98 High energy quantum scattering, eikonal approximation 98 High energy quantum scattering, semiclassical approximation 98 Homogeneous equation 60 61 Householder method 115 Hydrodynamics, steady state 158ff Hydrogenic orbital 76 84 Hyperbolic fixed points 42 Impact parameter 20 98 129 Implicit methods, ordinary differential equations 30 Implicit methods, parabolic partial differential equations 174 Inaccuracy, ordinary differential equations 26 Infinite lattice, Ising model 217 Inhomogeneous term, differential equation 55 Initial value problem 26 Initial value problem, ordinary differential equations 26 58 Initial value problem, partial differential equation 169 172 Integrable Hamiltonian 38 Integrable singularities 10 Integrals, multi-dimensional 197 Integration see "Differential equations" "Quadrature" Interaction, coulomb 14 Interaction, van der Waals 14 Invariant torus 42 Inverse vector iteration 118 Inversion, matrix 109 Ising model 215ff Ising model, infinite lattice 217 Ising model, phase transition 218 220 Ising model, thermodynamic properties 215 Jump geometry, fluid flow 168 Kam theorem 42 Lagrange multiplier 77 124 182 Laguerre polynomials 87 Lanczos algorithm, eigenvalue problem 119 Lane — Emden equation 52 Laplace's equation 157ff Lattice gauge theories 221 Legendre polynomials 86 93 104 Legendre polynomials, recursion relations 86 Lennard — Jones potential 14ff 20 69 see Lenz — Jensen potential 101 Linear approximation 109 123 Linear combination, atomic orbitals 224 Linear congruential method, random numbers 205 Linear stability analysis for the Brusselator 191ff Liquid drop 126 Lissajous patterns 38 Lommel function 130 Lorentzian wavepacket 188 Low-energy atomic resonances 108 Low-energy scattering 103ff Magnetic field 215 Magnetic material 215 magnetization 217 Mass, Chandrasekhar 53 Matrix, determinant 110 112 Matrix, eigenvalue problem 112ff Matrix, Gaussian elimination and back substitution 175 Matrix, Householder method 115ff Matrix, inversion 109ff Matrix, inversion, equilibration 112 Matrix, inversion, Gauss — Jordan method 110 Matrix, inversion, numerical round-off error 112 Matrix, inversion, pivoting 111 Matrix, operations 109ff Matrix, reduction to tri-diagonal form 115ff Matrix, singular 111 Matrix, sparse 145 151 Matrix, tri-diagonal 151 175 Metropolis algorithm 210ff Metropolis algorithm, auto-correlation 214 219 Metropolis algorithm, thermalization 214 Metropolis algorithm, trial step size 213 Minimization of chi-square 123
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