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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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Mixed boundary conditions 146 Molecular, orbitals 223 Molecular, vibrations 14ff Molecule, 17 19 221ff Molecule, 17 Molecule, diatomic 14 Molecule, HD 17 Momentum transfer 98 121 Monte Carlo methods 197ff see Monte Carlo methods, errors 204 Monte Carlo methods, Green's Function 225 Monte Carlo methods, heat bath algorithm 220 Monte Carlo methods, Path Integral 225 Monte Carlo methods, Path Integral, drift function 226 Monte Carlo methods, Path Integral, harmonic-oscillator potential 230 Monte Carlo methods, uncertainty 198 Monte Carlo methods, weight function 100 Morse potential 19 222 Mott cross section 122 Multi-dimensional integrals 197 Multi-electron atoms 72 Multipole decomposition 79 Multistep methods 29 Navier — Stokes equation 159 Neumann boundary condition 146 150 178 Newton — Cotes quadrature formulas 7 Newton — Raphson root finding 12 No-flux boundary conditions 190 No-slip boundary condition 165 Non-linear, eigenvalue equations 72 Non-linear, equations 189 Non-linear, stability analysis 191 Normal mode solutions 64 191 Nozzle geometry, fluid flow 167 Nuclear, charge distribution 120ff Nuclear, form factor 121 Nuclear, structure 120 Numerov method 56 One-dimensional Schroedinger equation 15 67ff Open-shell systems, atomic 78 Optical theorem 100 Orbiting, scattering 23 Ordinary differential equation, first order 25ff Ordinary differential equation, first order, accuracy monitoring 32 Ordinary differential equation, first order, Adams — Bashforth, four-step method 30 Ordinary differential equation, first order, Adams — Bashforth, two-step method 29 Ordinary differential equation, first order, Adams — Moulton methods 31 Ordinary differential equation, first order, Euler's method 26 Ordinary differential equation, first order, implicit methods 30 Ordinary differential equation, first order, multistep methods 29 Ordinary differential equation, first order, predictor-corrector algorithms 31 Ordinary differential equation, first order, round-off error 36 Ordinary differential equation, first order, Runge — Kutta algorithms 72ff Ordinary differential equation, first order, Runge — Kutta algorithms, fourth-order 33 42 Ordinary differential equation, first order, Runge — Kutta algorithms, second-order 32 Ordinary differential equation, first order, Runge — Kutta algorithms, third-order 33 Ordinary differential equation, first order, stability 34ff Ordinary differential equation, first order, Taylor series 28 Ordinary differential equations, second order 56 Ordinary differential equations, second order, accuracy 68 Ordinary differential equations, second order, coupled first order 25 Ordinary differential equations, second order, Cowling's method 56 Ordinary differential equations, second order, initial value problem 58 Ordinary differential equations, second order, Numerov method 56 Over-relaxation 152 Parabolic partial differential equations 169ff Parabolic partial differential equations, accuracy 174 Parabolic partial differential equations, alternating-direction methods 180 Parabolic partial differential equations, explicit scheme 170 Parabolic partial differential equations, implicit scheme 174 Parabolic partial differential equations, instability 172 Parabolic partial differential equations, stability 174 175 Parabolic partial differential equations, two-dimensional 179ff Parabolic well potential 69 70 188 Partial differential equations 145ff Partial differential equations, elliptic 145ff Partial differential equations, hyperbolic 145 Partial differential equations, initial value problem 169 Partial differential equations, parabolic 145 169ff Partial wave decomposition 103ff Partition function 197 216 Path Integral Monte Carlo 225 Pattern selection 189 Pauli principle 14 73 221 Periodic, boundary conditions 158 Periodic, potentials 72 Perturbation theory, Rayleigh — Schroedinger 138 Phase shifts, scattering 104 Phase space 16 37 Phase transition, Ising model 218 220 Phase transition, schematic shell model 141 Plane wave, incident 97 Poisson distribution, random number generation 206 Poisson's equation 55 57 121 146 158 Polynomial approximations, Bessel function 87 Polynomials, Hermite 87 Polynomials, Laguerre 87 Polytropic equation of state 52 Potential 6—12 14 222 Potential, 230 Potential, 72 Potential, central 20 38 45 103 Potential, centrifugal 21 104 Potential, Coulomb 57 72 121 222 Potential, double-well 72 Potential, finite square-well 72 Potential, Fock 80 Potential, Gaussian well 101 188 Potential, harmonic-oscillator 230 Potential, Henon and Heiles 42 Potential, Lennard — Jones 14ff 20 69 Potential, Lenz — Jensen 101 Potential, Morse 19 222 Potential, parabolic well 69 70 188 Potential, periodic 72 Potential, square well 69 70 101 188 Predictor-corrector algorithms 31 Pressure forces 159 Profile function 100 129 Programs, how to use 231ff Pseudo-random numbers 205 Quadrature 1 6ff Quadrature, accuracy 8 9 Quadrature, Bode's rule 9 Quadrature, Gauss — Chebyshev 96 Quadrature, Gauss — Hermite 95 Quadrature, Gauss — Laguerre 94 Quadrature, Gauss — Legendre 94 102 Quadrature, Gaussian 85 92ff Quadrature, Gaussian, abscissae 95 Quadrature, Gaussian, weights 95 Quadrature, Monte Carlo methods 197ff Quadrature, Newton — Cotes 7 Quadrature, round-off error 8 9 Quadrature, Simpson's 9 Quadrature, Simpson's rule 7 Quadrature, Trapezoidal rule 7 Quantization, semiclassical 14ff Quantum scattering 96ff Quantum states, stationary 67 see Quasi-spin operators 136 Rainbow scattering 23 random number generation 205ff Random number generation, Gaussian (or normal) distribution 208 Random number generation, linear congruential method 205 Random number generation, Metropolis algorithm 210 Random number generation, Metropolis algorithm, correlations 214 219 Random number generation, Metropolis algorithm, thermalization 214 Random number generation, Metropolis algorithm, trial step size 213 Random number generation, Poisson distribution 206 Random number generation, pseudo-random 205 Random number generation, von Neumann rejection 207 Random walk 210 Rayleigh — Ritz variational principle 73 Rayleigh — Schroedinger perturbation theory 138 Recoil correction 131 Recursion relation, cylindrical Bessel function 87ff Recursion relation, Legendre polynomials 86 Recursion relation, spherical Bessel functions 92 Relativistic kinematics 47 122 Relaxation method, elliptic partial differential equations 154 Residual interactions 134 Reynolds number, lattice 163 Reynolds number, physical 163 Root-finding 11ff 113 Root-finding, convergence 13 Root-finding, Newton — Raphson 12 Root-finding, secant method 12 Root-finding, simple search 11 Round-off error, boundary value problem 60 61 Round-off error, differentiation 4 Round-off error, eigenvalue problem 186 Round-off error, forward recursion of Bessel functions 90 Round-off error, matrix inversion 112 Round-off error, ordinary differential equations 36 Round-off error, quadrature 8 9 Runge — Kutta algorithms 32ff Runge — Kutta algorithms, fourth-order 33 42 Runge — Kutta algorithms, second-order 32 Runge — Kutta algorithms, third-order 33 Rutherford cross section 121 Scattering, amplitude 97 Scattering, amplitude, Born 98 Scattering, amplitude, eikonal 99 Scattering, angle 20 Scattering, classical 20ff Scattering, Dirac 129 Scattering, electron 96ff 103ff 102ff Scattering, high energy electrons 96ff Scattering, low-energy electrons 103ff Scattering, orbiting 23 Scattering, phase shifts 104 Scattering, quantum-mechanical 96ff Scattering, rainbow 23 Schematic shell model 134ff Schematic shell model, phase transition 141 Schematic shell model, semiclassical method 139 Schematic shell model, tunneling 142 Schroedinger equation, time-dependent 146 169 186ff 221 Schroedinger equation, time-dependent, tunneling 188 Schroedinger equation, time-independent 15 67ff 97 103 146 181 221 searches see "Root finding" Secant method, eigenvalue problem 65 Secant, root-finding 12 Second quantization 135 Second-order ordinary differential equations, Numerov method 56 Self-consistent field approximation 72 Semiclassical, method, schematic shell model 139 Semiclassical, quantization 14ff Semiclassical, scattering 98 Separable Hamiltonians 38 Separatrix 42 Shell model, schematic 133 Shooting method, boundary value problem 64 67 Simple search, eigenvalue problem 65 Simple search, root finding 11 Simpson's 9 Simpson's rule 7 Single-particle wave function 72 Singular matrix 111 Singularities, integrable 10 Sirius B 53 Slater determinant 73 Solar mass and radius 51 Sparse matrix 145 151 Special functions 85ff Special functions, recursion relations 86ff Specific heat 217 Spherical Bessel functions 92 104 Spherical geometry, elliptic partial differential equation 156 Spin degrees of freedom 215 Spin state, electron 73 square well potential 69 70 101 188 Stability analysis, non-linear equations 191 Stability, ordinary differential equations 34ff Stability, parabolic partial differential equation 175 Stability, partial differential equation 174 Stars, 40 Eri B 53 Stars, Sirius B 53 Stars, Stein 2051 53 Stars, white dwarf 46ff Stationary quantum states 67 Steady state hydrodynamics 158ff Stein 2051 53 Stream, function 161 Stream, lines 161 Stretched string 64 SU(2) group 136 Surface of section 39 Susceptibility, magnetic 217 Taylor series 2 28 Temperature distribution 157 Thermalization, Metropolis algorithm 214 Thermodynamic properties, Ising model 215 Thomas — Fermi model of the atom 101 Time-dependent Schroedinger equation 146 169 186ff 221 Time-independent Schroedinger equation 15 67ff 97 103 146 181 221 Torus 41 Torus, invariant 42 Total cross section 97 Trajectory 38 Trapezoidal rule 7 Tri-diagonal matrix 113 151 175 Tri-diagonal matrix, Householder method 115 Tri-diagonal matrix, matrix reduction to 115 Trial step size, Metropolis algorithm 213 Tunneling, schematic shell model 142 Tunneling, time-dependent Schroedinger equation 188 Uncertainty, Monte Carlo methods 198 Uncertainty, nuclear charge density parameters 125 Under-relaxation 152 Unitary evolution operator 187 valence electrons 78 Van der Waals interaction 14 Variational, calculation, treatment of two-electron system 76 Variational, calculus 77 Variational, energy, 223 Variational, principle 148 Variational, wave function, 224 Vibrations 146 Vibrations, molecular 14ff Virial theorem 77 81 viscosity 159 von Neumann rejection, random number generation 207 Vortex 167 Vorticity 161 Wake 162 Wave function, quantum state, stationary 67 Wave function, single-particle 72 Wave function, WKB 70 Weight function, Monte Carlo 200 Weights, gaussian quadrature 95 White dwarf stars 46ff WKB, approximation 16 WKB, wave function 70 wronskian 62
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