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Schweizer W. — Numerical quantum dynamics
Schweizer W. — Numerical quantum dynamics

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Название: Numerical quantum dynamics

Автор: Schweizer W.

Аннотация:

This book describes computational methods used in quantum dynamics with emphasis on small quantum systems. Computational physics is a fundamental physical discipline at the forefront of physical research. Thus it is an indisputable fact that computational physics form part of the essential landscape of physical science and education. In the present state of scientific knowledge the importance of quantum dynamics is commonplace. Computational quantum dynamics involves the use of computer calculations and simulations to solve quantum physical problems. Following a brief introduction to quantum dynamics the book revisits approximation techniques based on perturbational theory and variationalmethods. This discussion includes Hartree-Fock and density functional theory and quantum Monte Carlo methods. The next chapter presents the concepts of finite differences. Central in this chapter is the discretization in time and space. Later chapters concentrate on discrete variable techniques based on orthogonal polynomials, finite element and B-splinemethods for both time-independent and time-dependent problems and the combination of different computational techniques. The final chapter contains a list of useful sources for computational software and program codes. This book is primarily aimed at advanced students and graduates and researchers in theoretical and computational physics or chemistry and bridges the gap between quantum textbooks and computational research. Although not essential, the reader should have a basic background in quantum physics and some knowledge of numerical analysis would be helpful in reading this book.


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 267

Добавлена в каталог: 21.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
3j-symbol      11 14
Absorption      91
Adam — Bashforth algorithm, 4th order      139
Adam — Moulton algorithm, 4th order      139
Adams — Bashforth algorithm      139
Adams — Moulton algorithm      139
Aitken’s $S^2$ process      59
Alkali atoms      187—188
Alkali atoms, external fields      187
Alkali-like ions      188
Angular coordinates      162
angular momentum      9
Angular momentum, coupling      10
Angular momentum, SO(4, 2, R)      79
Anharmonic oscillator      182
Anharmonic oscillator, 1st order perturbation      183
Anharmonic oscillator, DVR      183
Anharmonic oscillator, parity      184
Antisymmetrizer      106
Associated Legendre function      10 161 168
Associated Legendredifferential equation      170
Avoided crossing      37 62
Azimuthal symmetry      161
B-splines      232
Bessel function      176
Bessel function, ordinary      176
Bessel function, Rodrigues formula      177
Bessel function, spherical      176
Bias      258
Bohr N.      2
Bohr — Sommerfeld quantization      2
Boor — Cox recursive formula      233
Born — Oppenheimer approximation      46 111
Bound states      6
Boundary condition, Dirichlet      210
Boundary condition, generalized von Neumann      210
Boundary value problem      210
Bra      8
Campbell — Baker — Hausdorff theorem      18
Cayley approximation      17
Cayley method      141
Chaos      35
Chebyshev polynomial      182
Christoffel — Darbaux relation      158
Christoffel — Darboux relation      167
Clebsch — Gordan coefficient      10
Commutator      4
Complex coordinate method      6 250
Complex coordinate rotation      7 164 250
Confluent hypergeometric equation      181
Confluent hypergeometric function      181
Constant of motion      35
Contact potential      2
Continuous states      6
Coordinates, Cartesian      39
Coordinates, cone      45
Coordinates, cylindrical      42
Coordinates, ellipsoidal      44
Coordinates, elliptic      46
Coordinates, elliptic cylindrical      44
Coordinates, hyperspherical      48
Coordinates, Jacobi      48
Coordinates, oblate spheroidal      44
Coordinates, parabolic      42
Coordinates, paraboloidal      44
Coordinates, polar      48
Coordinates, prolate spheroidal      44
Coordinates, semiparabolic      45
Coordinates, semiparabolic cylindrical      44
Coordinates, spherical      40
Coulomb integral      115
Coulomb systems      187
Crank — Nicholson approximation      17
De Broglie L.-V.      1
De Broglie relation      2
Defolded spectrum      38
Degenerate perturbation theory      60
Density functional theory      95 106
Density matrix      21
Density operator      20—21
Dipole strength      193
Direct product basis      160
Dirichlet boundary condition      210
Discrete variable representation      156 159
Discrete variable representation, fixed-node boundary condition      196 198
Discrete variable representation, hermite polynomial      183
Discrete variable representation, Legendre polynomial      189
Discrete variable representation, Legendre polynomial, cylindrical symmetry      191
Discrete variable representation, periodic      196 199
Discrete variable representation, spectroscopic quantities      193
Discrete variable representation, time-dependent systems      195
Discrete variable representation, wave packet propagation      195
DVR      159
Dynamical group      78
Dynamical Lie algebra      78
Dyson series      16
Ehrenfest’s theorem      20
Einstein A.      1
EISPACK      258
Energy-time uncertainty relation      89
Euler angles      11
Euler method, explicit      134
Euler method, implicit      134
Euler methods      134
Euler theorem      109
Exchange integral      115
expectation value      4
FBR      159
Fermion problem      125
Fermi’s Golden Rule      90
Feynman path integral      126
Finite basis representation      156 159
Finite differences, bound states      146
Finite differences, bound states, Poschl — Teller potential      147
Finite differences, Hamiltonian action      140
Finite differences, propagation      140
Finite differences, propagation, potential wall      146
Finite element matrix, dimension      227
Finite element matrix, non-vanishing elements      227
Finite elements      209 211
Finite elements, adaptive methods      230
Finite elements, error      230
Finite elements, rectangular      235
Finite elements, selfadaptive methods      230
Finite elements, splines      232
Finite elements, triangular      235
Finite elements, triangular, local coordinates      235
Finite elements, two-dimensional      235
Fixed-node method      125
Fractional charge      43
Free electron, magnetic field      203
Galerkin principle      212
Gauss quadrature      167
Gauss theorem      181
Gauss — Chebyshev quadrature, 1st kind      199
Gauss — Chebyshev quadrature, 2nd kind      198
Gauss — Symplectic — Ensemble      68
Gauss — Unitary — Ensemble      68
Gaussian orthogonal ensemble      68
Gear algorithm      139
Gegenbauer polynomials      177
Gegenbauer polynomials, generating function      177
Gegenbauer polynomials, Rodrigues formula      178
Generalized Laguerre polynomial      171
Generating function      167
Guiding function      124
Hahn polynomials      180
Hamiltonian      6
harmonic oscillator      182
Hartree equation      105
Hartree — Fock equation      106
Hartree — Fock method      95 104
Heisenberg uncertainty      89
Heisenberg uncertainty relation      4
Hellman — Feynman theorem      109
Hermite interpolation polynomial      220
Hermite interpolation polynomial, extended      222
Hermite mesh      200
Hermite polynomial      174
Hermite polynomial, finite elements      215
Hermite polynomial, generating function      174
Hermite polynomial, Jacobi matrix      175
Hermite polynomial, parity      175
Hermite polynomial, Rodrigues formula      174
Homogeneous function      108
Husimi function      23
Hydrogen atom, electric field      43
Hydrogen atom, external fields      62
Hydrogen atom, extremely strong magnetic field      203
Hydrogen atom, finite elements, two-dimensional      244
Hydrogen atom, strong external fields      187
Hydrogen eigenstates, boson representation      79
Hydrogen molecule-ion      46
Hylleraas ansatz, helium      99
Hypergeometric functions      180
Hypergeometric series      180
Hypervinaltheorem      111
IMSL      257
Inner product      8
Integrability      35
Interpolation polynomial, degree of freedom      227
Interpolation polynomial, two-dimensional, cubic      239
Interpolation polynomial, two-dimensional, linear      237
Interpolation polynomial, two-dimensional, quadratic      238
Interpolation polynomial, two-dimensional, quartic      241
Interpolation polynomial, two-dimensional, quintic      240
Jacobi matrix      167
Jacobi polynomial      14 181
Jacobi polynomial, generating function      182
Kepler problem      49
Ket      8
Kicked systems      141
Kohn — Sham equations      107
Krylov space      103
Kustaanheimo — Stiefel coordinates      51—52
Kustaanheimo — Stiefel transformation      51—52
l/N-shift expansion      70
Lagrange interpolation polynomial      217
Lagrange interpolation polynomial, linear equations      218
Lagrange interpolation polynomial, n-th order      218
Laguerre mesh      200—201
Laguerre mesh, modified      202
Laguerre polynomial      171 175
Laguerre polynomial, finite elements      215
Laguerre polynomial, generalized      171
Laguerre polynomial, generating function      172
Laguerre polynomial, Jacobi matrix      172
Laguerre polynomial, Rodrigues formula      171
Lanczos method      101
Lanczos method, algorithm      102
Lanczos method, spectrum transformation      101
Lanczos, software      259
Landau function      203
LAPACK      258
Laplace — Beltrami operator      39
Laplace — Beltrami operator, cylindrical coordinates      42
Laplace — Beltrami operator, elliptic coordinates      47
Laplace — Beltrami operator, parabolic coordinates      42
Laplace — Beltrami operator, polar coordinates      51
Laplace — Beltrami operator, semiparabolic coordinate      45
Laplace — Beltrami operator, spherical coordinates      40
LDA      107
Leap-frog algorithm      135
Legendre differential equation      170
Legendre function, associated      168
Legendre function, parity      171
Legendre polynomial      168 187
Legendre polynomial, generating function      171
Legendre polynomial, Jacobi matrix      170
Legendre polynomial, Rodrigues formula      168
Legendre polynomials      161
Level repulsion      37
Lie algebra, dynamical      78
Lie algebra, spectral generating      78
Liouville equation      22
Local basis      213
Local basis, local matrices      225
Local density approximation      107
Maple      256
Mathematica      257
MATLAB      256
Mesh calculation      200
Mesh, Laguerre      200
Metropolis algorithm      121
Model potentials      188
Monte Carlo method      118
Monte Carlo method, important sampling      121 124
Monte Carlo method, quantum      118
Monte Carlo method, quantum, diffusion      123
Monte Carlo method, quantum, guiding function      124
Monte Carlo method, quantum, path integral      128
Monte Carlo method, quantum, variational      122
Moyal brackets      24
Muller method      179
Murphy equation      170
N-particle systems      48
NAG      257
Nearest neighbor distribution      37 65
Neumann series      16
Newton’s method      179
Noether’s theorem      36
Non-integrable systems      35
Numerov integration      164
Numerov method      150—151
Numerov method, eigenvalue problem      151
Ordinary Bessel function      176
Orthogonal polynomials      165
Orthogonal polynomials, three-term recurrence relation      166
Orthogonal polynomials, zeros      166
Orthonormal polynomials      165
Oscillator strength      193
Oscillator, anharmonic      182
Oscillator, harmonic      182
Partial differential equation, elliptic      3
Partial differential equation, hyperbolic      3
Partial differential equation, parabolic      3
Particle-in-boxeigenfunction      198
Perturbation theory      55
Perturbation theory, degenerate      60
Perturbation theory, Rayleigh — Schrodinger      56
Perturbation theory, two-fold degenerate      61
Phase space      35
photoelectric effect      2
Photoelectron      2
photons      2
Planck constant      2
Planck M.      1
Planck — Einstein relations      2
Pochhammer symbol      180
Poisson bracket      35
Poisson distribution      38 65 120
Polar coordinate      51
Polarization      194
Polarization, $\pi$      194
Polarization, $\sigma^+$      194
Polarization, $\sigma^-$      194
Pollaczek polynomials      180
Poschl — Teller potential      147
Predictor-corrector method      139
Probability conservation      5
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