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Adhikari S.K. — Variational Principles and the Numerical Solution of Scattering Problems
Adhikari S.K. — Variational Principles and the Numerical Solution of Scattering Problems



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Íàçâàíèå: Variational Principles and the Numerical Solution of Scattering Problems

Àâòîð: Adhikari S.K.

Àííîòàöèÿ:

The first coherent treatment of the subject in nearly two decades—an important working resource for researchers and a superior graduate-level text Variational Principles and the Numerical Solution of Scattering Problems is designed to serve as both a professional guide and a self-contained graduate-level text. Writing at a level accessible to students with a knowledge of basic quantum mechanics, Dr. Sadhan K. Adhikari treats most major numerical methods for solving scattering problems. While the emphasis is on variational methods, Dr. Adhikari also discusses important nonvariational methods and their applications to realistic problems in molecular, atomic, and nuclear physics. The first part of the book presents the major variational principles and numerical methods for scattering, using a pedagogic style appropriate to graduate courses. The remaining parts, especially useful to researchers interested in performing scattering calculations, include: Applications of variational principles in realistic multichannel problems Numerical applications of the methods described to realistic scattering problems Up-to-date reviews of recent benchmark scattering calculations Variational Principles and the Numerical Solution of Scattering Problems is an important working reference for physicists involved with scattering problems as well as graduate students in nuclear, atomic, and molecular physics. It saves hours of searching the world literature on the subject and provides a direct connection to contemporary numerical approaches to solving scattering problems.


ßçûê: en

Ðóáðèêà: Ôèçèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1998

Êîëè÷åñòâî ñòðàíèö: 323

Äîáàâëåíà â êàòàëîã: 20.03.2010

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Anomalous behavior      134—136 215—219
Anomalous behavior in complex Kohn method      219
Anomalous behavior in inverse Kohn method      134—136
Anomalous behavior in Kohn method      134—136
Anomalous behavior in Newton method      217
Anomalous behavior in Schwinger method      216—217
Asymptotic, behavior of Green’s function      22 26
Asymptotic, behavior of Lippmann — Schwinger, equation      25—27
Asymptotic, behavior of spherical Bessel and, Neumann functions      15—16 26
Asymptotic, behavior of wave function      12 14 16—17 47 50
Asymptotic, boundary condition      11 14
Atom-diatom collision (reactive)      248—249 237—240 300—304
Atom-diatom collision (reactive), complex Kohn method      248—249 301 304
Atom-diatom collision (reactive), Newton method      237—240 300—304
Atomic unit      261
Basis functions, $L_2$      5
Basis functions, Kohn method      115—116 138
Basis functions, Schwinger method      170—171
Born or Neumann (series) for bound state      92
Born or Neumann (series) for distorted wave      194
Born or Neumann (series) for scattering      69 80—84 160 256
Born or Neumann (series) for T matrix      79 83 213 269—271
Born or Neumann (series) for wave function      34
Born or Neumann (series), approximation      29—30 57 80
Bound-state, approximation      51
Bound-state, scattering approach, for      91—94
Channel      5—6
Channel, open      51
Close-coupling (CC) equations      9 43 49—54 63 85 225—226
Close-coupling (CC) equations for K matrix      56
Close-coupling (CC) equations for t matrix      53 227—229
Close-coupling (CC) equations for wave function      52
Close-coupling (CC) equations, electron-helium scattering      290
Close-coupling (CC) equations, electron-hydrogen scattering      284
Close-coupling (CC) equations, partial-wave      54—56
Close-coupling (CC) equations, positron-helium scattering      293
Close-coupling (CC) equations, positron-hydrogen scattering      286
Close-coupling (CC) equations, post      53—54
Close-coupling (CC) equations, prior      53—54
Collision      3 319
Contour deformation technique      68
Cross section, electron-helium scattering      291
Cross section, electron-hydrogen scattering      280
Cross section, multichannel      59—60
Cross section, partial-wave      18—20
Cross section, reaction      19
Cross section, total      20
Effective range      42
Electron-helium scattering      288—292
Electron-helium scattering, Bethe — Goldstone method      289
Electron-helium scattering, Born formula      291
Electron-helium scattering, close-coupling (CC) method      290
Harris method      282
Harris method, Born formula for phase shift      281
Harris method, close-coupling (CC) approach      281 284
Harris method, Electron-hydrogen scattering      280—285
Harris method, optimized anomaly-free method      289
Harris method, polarizability      290—291
Harris method, polarized-orbital method      289
Harris method, resonance      290—291
K matrix      36
K matrix, half-shell      77—78
K matrix, off-shell      159
K matrix, principal-value treatment      68 71—74 86
K matrix, unitarity      41
Kernel, compact      24 64
Kernel, Fredholm      24 43 50 63—69 76
Kernel, Hilbert — Schmidt      24 44
Kohn method      297
Kohn method for resonance      95—97
Kohn method, $CO, C02$      299—300
Kohn method, complex Kohn method      298
Kohn method, continuum orbitals      249—253
Kohn method, degenerate-kernel method      106 179
Kohn method, Electron volt      261
Kohn method, Electron-molecule scattering      297—300
Kohn method, Faddeev — Yakubovskii equation      9 40
Kohn method, Feshbach projection operator technique, Kohn method      190
Kohn method, Fock coupling scheme      50
Kohn method, Fredholm      7 62—69 76 79
Kohn method, Green’s function, incoming-wave      22—23
Kohn method, Hartree — Fock, wave function      249—250
Kohn method, Huck model      272
Kohn method, hydrogen $(H_2)$      297—298
Kohn method, i?-matrix method      297—299
Kohn method, Integral equation      7
Kohn method, Integration quadratures      66 72
Kohn method, Ionization      4
Kohn method, iterative Schwinger method      298 300
Kohn method, method of moments      103—104
Kohn method, multichannel      87—90
Kohn method, nitrogen $(N_2)$      298
Kohn method, nonsingular      74—80
Kohn method, numerical results      280—285
Kohn method, outgoing-wave      22—23
Kohn method, phase shift      283
Kohn method, polarizability      281 283
Kohn method, polarized orbital method      282
Kohn method, principal-value      37—38 73
Kohn method, resonances      282—283
Kohn method, Schwinger (multichannel) method      297—300
Kohn method, Schwinger multichannel method      229—234
Kohn method, T matrix      8—9 74—80
Kohn method, variational principle      210—215
Kohn method, variational principles      101—107
Lippmann — Schwinger equation      7 21
Lippmann — Schwinger equation for K matrix      39 40
Lippmann — Schwinger equation for t matrix      28 31
Lippmann — Schwinger equation for wave function      23
Lippmann — Schwinger equation, (iterative) Born — Neumann series, solution      7—8 34 80
Lippmann — Schwinger equation, asymptotic behavior      25—27
Lippmann — Schwinger equation, multiparticle      43 49
Lippmann — Schwinger equation, nonuniqueness of solution      44 45
Lippmann — Schwinger equation, numerical solution      65—74
Moller operator      12
Neumann series      (see “Born series”)
Newton method      267—268 276—277 300—304
Newton method, nucleon-nucleon scattering      275—278
Newton method, optimized anomaly-free method      265—266 282—283
Newton method, optimized minimum-norm method      265—266 282—283
Newton method, positron-helium scattering      292—294
Newton method, positron-hydrogen scattering      285—288
Newton method, principal-value treatment      71—74
Newton method, Schwinger $L_2$ method      265—266
Newton method, Schwinger (iterative) method      269—271
Newton method, Schwinger basis-set method      263—267 276—279
Newton method, separable expansion      69 276—279
Newton method, single-channel study      261—272
Newton method, variational (basis-set) method      69 263—269
Numerical solution of integral equation, atom-diatom (reactive) scattering      300—304
Numerical solution of integral equation, complex Kohn method      267—268 278 301 304
Numerical solution of integral equation, degenerate-kernel scheme      69
Numerical solution of integral equation, electron-atom scattering      294—295
Numerical solution of integral equation, electron-helium scattering      288—292
Numerical solution of integral equation, electron-hydrogen scattering      280—285
Numerical solution of integral equation, electron-molecule scattering      297—300
Numerical solution of integral equation, explicit matrix elements      258—261
Numerical solution of integral equation, four-nucleon scattering      278
Numerical solution of integral equation, inverse Kohn (minimum-norm) method      265—266 282—283
Numerical solution of integral equation, Kohn (anomaly-free) method      265—266 282—283
Numerical solution of integral equation, Kohn (minimum-norm) method      265—266 282—283
Numerical solution of integral equation, Kohn (off-shell) method      263 265—267
Numerical solution of integral equation, Kohn (on-shell) method      263 281—283
Numerical solution of integral equation, molecular photoionization      296—297
Numerical solution of integral equation, multichannel model      272—275 284—285
Numerical solution of integral equation, neutron-deuteron scattering      278
Numerical solution of integral equation, T matrix (iterative)      269—271 278—279
Pade approximation      69 84 256 279
Partial-wave (expansion), Born phase shift formula      281 291
Partial-wave (expansion), Green’s function      25
Partial-wave (expansion), K matrix      40
Partial-wave (expansion), multichannel      54—56
Partial-wave (expansion), scattering amplitude      18
Partial-wave (expansion), scattering cross section      18
Partial-wave (expansion), t matrix      32—35
Partial-wave (expansion), wave function      15—16 38
Partition      5—6
Photodisintegration of triatomic molecule      240—245
Photoionization      202 210
Photoionization, frozen-core Hartree — Fock method      252—253
Positron-helium scattering      292—294
Positron-helium scattering, close-coupling (CC) method      293
Positron-helium scattering, Kohn method      292
Positron-helium scattering, polarizability      292
Positron-helium scattering, resonance      294
Positron-hydrogen scattering      285—288
Positron-hydrogen scattering, close-coupling (CC) method      286
Positron-hydrogen scattering, complex-energy extrapolation      286
Positron-hydrogen scattering, Harris method      286—287
Positron-hydrogen scattering, Kohn method      285—287
Positron-hydrogen scattering, resonance      288
S matrix      18 31—32 192
S matrix, unitarity      32 57
Scattering, amplitude      14 18 27
Scattering, breakup      3
Scattering, complex potential      85—87
Scattering, cross section      15 18 27
Scattering, distorted wave      193—196
Scattering, eigenphase      57
Scattering, elastic      3
Scattering, electron-atom      255 294—295
Scattering, electron-helium      288—292
Scattering, electron-hydrogen      280—285
Scattering, few-particle      69—70
Scattering, four-nucleon      70 278
Scattering, Green’s function      21—23
Scattering, helium atom      288—294
Scattering, hydrogen atom      279—288
Scattering, inelastic      4
Scattering, length      42
Scattering, multichannel      7 42—60 272—275 284—285
Scattering, nonsingular equation      74—80
Scattering, nucleon-nucleon      255 276—278
Scattering, off-shell      65 159
Scattering, on-shell      65 159
Scattering, phase shift      16—17 34 41
Scattering, positron-hydrogen      285—288
Scattering, potential      3
Scattering, reactive (rearrangement)      3—4 237—240 300—304
Scattering, threshold      4
Scattering, time-independent description      10—13
Scattering, wave-function description      13—27
Scattering, wave-packet description      11
Schwinger method      285—287
Schwinger method, Potential, exponential      261 265 267 269—271
Schwinger method, Reaction cross section      19
Schwinger method, Resonance      36 77 91—96
Schwinger method, Rydberg      261
Schwinger method, Yukawa      261 263 269—271
Separable expansion      257 277—278
Separable expansion, analytic      175
Separable expansion, Bateman      174—175
Separable expansion, energy-dependent      175—176
Separable expansion, Ernst — Shakin — Thaler      175
Separable expansion, Hilbert — Schmidt      173—174
Separable expansion, unitary pole      172—173
Spherical Bessel and Neumann functions      15—16
Spherical Bessel and Neumann functions, half-shell      77—78 159
Spherical Bessel and Neumann functions, hermitian analyticity      30
Spherical Bessel and Neumann functions, post      52—54
Spherical Bessel and Neumann functions, prior      52—54
Spherical Bessel and Neumann functions, t (transition) matrix      18 27
Two-potential formula      196
Unitarity cut      30 35
Variational principle (method), anomalous behavior      215—219
Variational principle (method), anomaly      109 134—136
Variational principle (method), anomaly-free      136—137
Variational principle (method), anomaly-free Kohn      219—222
Variational principle (method), basis-set      108 115—134
Variational principle (method), complex Kohn (rearrangement)      248—249
Variational principle (method), complex Kohn (t matrix)      161—162 186—192 267—268 276—278
Variational principle (method), complex Kohn multichannel      245—249 301 304
Variational principle (method), distorted wave      193—198
Variational principle (method), fractional      160 162 164 165 178
Variational principle (method), general matrix element      201—210
Variational principle (method), Green’s function      188—189
Variational principle (method), Harris      109 128—132 282 286—287 289
Variational principle (method), higher-order      183—186
Variational principle (method), Hulthen      108 112 114 123—124 130—132
Variational principle (method), insertion technique      199—201
Variational principle (method), integral equation      101—107
Variational principle (method), inverse Kohn      108—109 113 121—122 124 130—132
Variational principle (method), iterative scheme      180—182
Variational principle (method), Kato identity      113
Variational principle (method), Kohn      107—122 124 130—132 263 281—283 285—287 292
Variational principle (method), Kohn (anomaly-free)      136—137 265—266 273—275
Variational principle (method), Kohn (K matrix)      106 161—162 186—187 263 265—268
Variational principle (method), least squares      154—157
Variational principle (method), minimum-norm inverse Kohn      132—134 265—266 282—283
Variational principle (method), minimum-norm Kohn      132—134 265—266 273—275 282—283
Variational principle (method), multichannel i?-matrix      145—147
Variational principle (method), multichannel inverse Kohn      143—145
Variational principle (method), multichannel Kohn      137—143 273—275
Variational principle (method), Newton      106 160 176—180 257 267—268 276—278
Variational principle (method), Newton (distorted wave)      197—198
Variational principle (method), Newton basis-set      178—180
Variational principle (method), Newton, iterative      180—182
Variational principle (method), Newton, multichannel inelastic      234—237
Variational principle (method), Newton, multichannel reactive      237—240 300—304
Variational principle (method), Newton, photodisintegration of, triatomic molecule      240—245
Variational principle (method), Newton, with insertion      200—201
Variational principle (method), off-shell      8 159—162
Variational principle (method), on-shell      8 99
Variational principle (method), optimized anomaly-free      148—150 152—154 265—266 282—283 289
Variational principle (method), optimized minimum-norm      148—152 265—266 282—283
Variational principle (method), R matrix      109 124—128 145—147 193 290
Variational principle (method), Rayleigh — Ritz      107 109—111 128—129
Variational principle (method), Rubinow      (see “Inverse Kohn”)
Variational principle (method), Schwinger      103 160 162—176 257 262—267 276—278 285—287
Variational principle (method), Schwinger (distorted wave)      197
Variational principle (method), Schwinger (K matrix)      162 164 262—267
Variational principle (method), Schwinger, iterative      180—182 207—208 269—271
Variational principle (method), Schwinger, multichannel      227—234 273—275 284—285
Variational principle (method), Schwinger, with insertion      199—201
Variational principle (method), T matrix      161 210—215
Variational principle (method), trilinear      160
Virtual states      36 96—97
Wave function, incoming-wave      23
Wave function, outgoing-wave      23
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