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Hartree D.R. — The calculation of atomic structures
Hartree D.R. — The calculation of atomic structures



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Название: The calculation of atomic structures

Автор: Hartree D.R.

Аннотация:

Judging by the enquiries I have had during the past four years for results of calculations of atomic structures and for information on methods of carrying out such calculations, there seems to have been a revival of interest recently in this subject. Without evidence of such interest, I would hardly have ventured to choose it as the subject for a series of lectures which I was invited to give as a Philips Visitor to Haverford College in the early part of the spring semester of 1955, since much of the material for such a series dates from before the war, and might now seem somewhat old-fashioned. However, that material has never been collected, except in a rather condensed form in a review article (Reports on Progress in Physics, 11, 113, 1948), and very little information was given there on practical methods for carrying out the calculations. Further, there has been some recent work in the subject, and the rapid development, since the war, of automatic digital calculating machines, and of methods of programming for them, promises to make practicable many calculations in this field which would be impracticable without the assistance that such machines provide.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 181

Добавлена в каталог: 26.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$      22 26 27 28 29 31 33 39 49 103 106 107 110 113 136 156 160
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$ as approximation to energy E      25 136—145 156
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$ as Lagrange parameter      26
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, contribution to, from $(np)^{6}$ group      48
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, definition      22 27 28 29
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, formula for configuration of complete groups      49
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, formula for many-electron system      45
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, formula for two-electron system      33 34
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, formula for, for configuration including incomplete groups      103 106 110
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, stationary values of      25 28 29 34 36
$E' = \int\Psi^{*} H\Psi dr / \int\Psi^{*}\Psi dr$, variation of      24—29 35 52—54 112 137
$F_{k}(nl, n'l')$ integrals      33 46 110 138
$F_{k}(nl, n'l')$ integrals, variation of, with P(nl)      35 52 53
$G_{k}(nl, n'l')$ integrals      46 110 138
$G_{k}(nl, n'l')$ integrals, variation of, with P(nl)      53
$h^{2}$ extrapolation (Richardson extrapolation)      75
$r_{ij}$ (distance between two electrons)      15 32 43 46 150 153 155 156
$r_{ij}$ (distance between two electrons), dependence of wave function on      153 155—159
$r_{ij}$ (distance between two electrons), expansion of reciprocal of      46
$r_{ij}$ (distance between two electrons), retardation of field depending on      150
$Y_{k}(nl, n'l'; r)$ functions      50 77 90 91
$Y_{k}(nl, n'l'; r)$ functions, behavior for small r      92 96
$Y_{k}(nl, n'l'; r)$ functions, calculation of      79 89 91 92
$Y_{k}(nl, n'l'; r)$ functions, definition of      50
$Y_{k}(nl, n'l'; r)$ functions, equations for      51 89
$Z_{0}(nl, nl; r)$ functions      77
$Z_{0}(nl, nl; r)$ functions, behavior of, for small r      79
$Z_{0}(nl, nl; r)$ functions, initial estimates of      78 132
$Z_{0}(nl, nl; r)$ functions, interpolation of, with respect to atomic number      132
$Z_{0}(nl, nl; r)$ functions, revision of estimates of      78 87
$Z_{0}(nl, nl; r)$ functions, scaling of      116 117
$Z_{k}(nl, nl; r)$ function      51 91
$Z_{k}(nl, nl; r)$ function, behavior of, for small r      92
$Z_{k}(nl, nl; r)$ function, calculation of      92
$Z_{k}(nl, nl; r)$ function, definition of      51
$\delta_{\alpha\beta}$ coefficients      40
$\epsilon_{\alpha\beta\gamma...}$ coefficients      40 43 44
(LS) terms      101 102—106 112 139
(nl) groups      19
(nl) groups, $(np)^{b}$ group, contribution to E'      48
(nl) groups, complete      19 39 45—50 59 110
(nl) groups, incomplete      20 102 110
(nl) groups, relativistic      149
Altmann, S.      99
Analytic wave functions      20 30 33 37 154 155 156 161
Atomic Energy Levels (National Bureau of Standards)      106
Atomic units      5 10 14 147
Baber, T.D.      157 159
Baker, E.B.      135
Bartlett, J.H.      157 158
Bates, D.R.      162
Bernal, M.J.M.      161
Biermann, l.      160 163
Bohr, N.      1 2 17
Boys, S.F.      161
Brenner, S.      151
Brillouin, L.      134
Brown, G.E.      150 151
Central-field wave functions, nonrelativistic      19 45 46 see
Central-field wave functions, nonrelativistic, (nl) groups of      19 20
Central-field wave functions, nonrelativistic, analysis of Hylleraas wave functions into      155
Central-field wave functions, nonrelativistic, complete groups of      19 39 45—50 54 110
Central-field wave functions, nonrelativistic, incomplete groups of      20 102 110
Central-field wave functions, nonrelativistic, variation with direction      9 10 11 19
Central-field wave functions, relativistic      147
Central-field wave functions, relativistic, (nl), (nl) subgroups of      149
Central-field wave functions, relativistic, variation with direction      147
Chandrasekhar, S.      156
Characteristic values, automatic determination of      85—87 175
Checking, of integration of a differential equation      69
Checking, of quadrature      67
Clendinin, W.W.      157 159
Clogston, A.M.      37
Cohen, E.R.      5
Configuration interaction, configuration mixing      see "Superposition of configurations"
Configuration, atomic      19 20 102 108 153
Confluent hypergeometric functions (Whittaker functions)      142 143
Coolidge, A.S.      29 156 157
Coulson, C.A.      37
Darwin, C.G.      147
Delbrueck, M.      19
Determinant wave functions (Slater determinants)      18 20 39 103 150
Determinant wave functions (Slater determinants), algebraical manipulation of      39—42
Digital computer      20 61 77 86 97 166
Dirac, P.A.M.      55 146 147
Douglas, A.S.      85 99 117 163
DuMond, J.W.M.      5
Duncanson, W.E.      37
Effective nuclear charge      117
Effective quantum number      141
Electron      1
Electron, classical radius of      5
Electron, rest energy of      6 148
Electron, spin of      2 11—13 146
Electrons, equivalence of      4 15 153
Eriksson, A.      159
Exchange      59 60
Exchange, Slater's approximate function for      60
Exclusion principle (Pauli principle)      2 16 17 18 149
Fermi, E.      134
Finite differences      63
Fock's equations (equations of self-consistent field with exchange)      55 68 72 90 140 159 160
Fock's equations (equations of self-consistent field with exchange), integrodifferential form of      57 140
Fock's equations (equations of self-consistent field with exchange), numerical solution of      90—97
Fock, V.      55 158
Fox, L.      73 76 151
Frank, J.      1
Froese, C.      93 128 131 174 175
Gill, S.      98
Goldberg, L.      37
Gombas, P.      134
Goodwin, E.T.      73 76 151
Goudsmid, S.      2
Green, L.C.      92 155 157
Gronwall, T.H.      158
Gyromagnetic effect      11
Hartree, D.R.      18 36 61 93 99 111 117 120 131 140 143 144 149 160
Hartree, W.      61 99 111 131 140 160
Hasse, H.R.      157 159
Haurwitz, E.S.      37
Helium atom      31 153—161
Hertz, G.      1
Herzberg, G.      156
Hydrogen negative ion ($H^{-}$)      153 156
Hydrogen- and hydrogen-like wave functions      38 116 118 123 133
Hylleraas, E.A.      155 156 159
I(nl) integrals      32 45 137
I(nl) integrals, substitution for P''(nl) in      137
I(nl) integrals, variation of, with P(nl)      35 52
Interpolation      64
Interpolation of wave functions with respect to atomic number      115
Iutsis, A.P.      161
j and J (total moment of momentum)      101 147
James, H.M.      29 156 157
l and L (orbital moment of momentum)      9 10 19 46 53 54 81 82 96 101 143 147 148
l and L (orbital moment of momentum), notation for values of      9 101 148
Lagrange multipliers      26 36 53 56
Lagrange multipliers, nondiagonal      56 58 90
Lamb shift      156
Legendre polynomials      46
Lennard-Jones, J.E.      55 157
Level      101
Lindsay, R.B.      36
Loewdin, P.O.      38 174
Luke, P.J.      157 159 160
Matching of solutions satisfying boundary conditions at r=0 and $r=\infty$      80 85 93—95 142 175
Mayers, D.F.      174
Meyerott, R.      157 159 160
Morse, P.M.      37
Normalization      7 18 26 33 35 42 80 87
Numerical integration      64—76
Numerical integration of first-order differential equation      73—76
Numerical integration of second-order differential equation      68—72
Numerical integration, Fox — Goodwin method for      73 76 151
Numerical integration, Numerov method for      71
Numerical integration, quadrature      64—67
Numerical integration, Runge — Kutta process      98
Numerov, B.      71
Olver, F.W.J.      72
Orthogonality      7 18 19 36 37 42 48 56 58 61 90
Orthonormal property      7 42 48 53
Parr, R.G.      155
Pauli, W.      2 16
Perturbation theory      22 104
Petrashen, M.J.      55
Piper, W.W.      175
Polarization      362
Pople, J.A.      157
Pratt, G.W.      61 114 174
Prener, J.S.      175
Quantum defect      141
Quantum defect, limiting, as n $n \rightarrow \infty$      144
Racah, G.      110 111
Radial wave equation, nonrelativistic      9 54 59 77 89 91 98 111 112
Radial wave equation, nonrelativistic, as two first-order equations      98
Radial wave equation, nonrelativistic, for configuration including incomplete groups      111
Radial wave equation, nonrelativistic, for configuration of complete groups      54
Radial wave equation, nonrelativistic, numerical integration of      80 93
Radial wave equation, nonrelativistic, numerical integration of, matching procedure in      80 85 93—95 142 175
Radial wave equation, nonrelativistic, numerical integration of, starting procedure in      81 82 95
Radial wave equation, nonrelativistic, numerical integration of, Torrance's method for      89
Radial wave equation, nonrelativistic, Riccati form for      99
Radial wave equation, nonrelativistic, with log r as independent variable      99
Radial wave equation, nonrelativistic, with superposition of configurations      161
Radial wave equations, relativistic      99 148
Radial wave equations, relativistic, first-order nonlinear form of      151
Radial wave equations, relativistic, numerical solution of      151 174
Radial wave equations, relativistic, relation to simultaneous first-order form of non relativistic equation      148
Radial wave functions P(nl; r)      9 19 31 45 111 115—124 128—132
Radial wave functions P(nl; r) of a single "series" ("valency") electron      140
Radial wave functions P(nl; r), equations for      see "Radial wave equations"
Radial wave functions P(nl; r), initial estimates of      78 115 117 118 120—124 128
Radial wave functions P(nl; r), interpolation of, with respect to atomic number      120 123
Radial wave functions P(nl; r), limiting behavior of, for large atomic number      118 119 128—132
Radial wave functions P(nl; r), mean radius of      116 120 125 126—129
Radial wave functions P(nl; r), median radius of      116 134
Radial wave functions P(nl; r), reduced      119—123 128—132
Radial wave functions P(nl; r), relativistic      148 150
Radial wave functions P(nl; r), revision of estimates of      87 90
Radial wave functions P(nl; r), scaling of      116 117
Richardson, L.F.      75
Ridley, E.C.      85 132 175
Ritz formula for series in optical spectra      144
Rosen, M.      135
Runciman, W.A.      99 117
Russell — Saunders coupling      101
Rutherford, E.      1
Sahni, R.C.      161
Scaling of wave functions      116 117
Schroedinger, E.      27
Screening numbers (screening parameters; shielding constants)      20 116 117 124 134 166
Screening numbers (screening parameters; shielding constants), Slater's rules for      20 126
Screening numbers (screening parameters; shielding constants), tables of      167
Screening numbers (screening parameters; shielding constants), variation with atomic number      124—128
Screening numbers (screening parameters; shielding constants), variation with atomic property      117 126
Self-consistent field      18
Self-consistent field with exchange      20 60 90
Self-consistent field without exchange      20 60 77
Self-consistent field, relativistic      150
Shortley, G.H.      103
Slater coefficients      46 47
Slater, J.C.      20 45 60 61 103 106 108 126
Sodium      121
Sodium, doublet structure in spectrum of      13 101
Spin-orbit interaction      13 42 102 146
Stationary states      1 2 22
Stern — Gerlach experiment      12
Stevenson, A.F.      159
Superposition of configurations      154 155 159—162
Swirles, B.      111 140 150 160
Taylor, G.R.      155
Ten-electron system      49 55
Ten-electron system, Fock's equations for      55
Ten-electron system, formula for E'      49
Term      101
Theory of Atomic Spectra (Condon and Shortley)      46 49 106 110 111 125 134 159
Thomas — Fermi approximation      134 135
Thomas, L.H.      134
Thomson, J.J.      1
Torrance, C.C.      88
Transition probabilities      3
Trefftz, E.      160 163
Two-electron system      30—37 153 155—159
Two-electron system, Hylleraas's approximate wave function for      156 158
Uhlenbeck, G.E.      2
Undheim, B.      159
Vallarta, M.      135
van Vleck, J.H.      162
Variation equations      84
Variation principle      22—38 39 52 104 107 150
Variation principle for configuration of complete groups      52
Variation principle for excited states      36
Variation principle for relativistic wave functions      150
Velocity of light      5 146 147
Watt, J.M.      166
Wave equation, for single particle in three dimensions      27 146
Wave equation, for system of electrons      15
Wave equation, for two particles      14 156
Wave equation, nonrelativistic (Schroedinger's equation), for electron      6
Wave equation, nonrelativistic (Schroedinger's equation), for single particle in one dimension      22
Wave equation, relativistic (Dirac's equations)      146
Wave functions      6
Wave functions for many-particle system      16 29
Wave functions, analytic      20 30 33 37 154 155 156 161
Wave functions, antisymmetrical      16 103
Wave functions, complex      11 28 29
Wave functions, criteria for approximate      29 157
Wave functions, determinantal      18 20 39 103 150
Wave functions, isotropic      19 160
Wave functions, normalized      7
Wave functions, orthogonal      7 19 47 53 56
Wave functions, orthonormal      7 42 48
Wave functions, relativistic      146
Wave functions, scaling of      116
Wave functions, single-product      17 60
Wave functions, symmetrical      16
Whitelaw, N.G.      162
Whittaker, E.T.      142 143
Williams, A.O.      150 159
Williamson, R.E.      29
Wilson, W.S.      36
Woodward, J.B.      151
Y(nl; r) function      54 77 80 91 93
Y(r) function      33 36 54 78 79
Yost, W.J.      89
Young, L.A.      37
Z(r) function      77
Z(r) function, contributions to      77 78 87 115 132
Z(r) function, definition of      77
Zeeman effect      12
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