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Bayfield J.E. — Quantum Evolution: An Introduction to Time-Dependent Quantum Mechanics
Bayfield J.E. — Quantum Evolution: An Introduction to Time-Dependent Quantum Mechanics



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Название: Quantum Evolution: An Introduction to Time-Dependent Quantum Mechanics

Автор: Bayfield J.E.

Аннотация:

A unique introduction to the concepts of quantum mechanics, Quantum Evolution addresses the present status of time-dependent quantum mechanics for few-body systems with electromagnetic interactions. It bridges between the quantum mechanics of stationary quantum systems and a number of recent advanced theoretical treatises on various aspects of quantum mechanics. The focus is on strongly-quantum and semi-classical systems, including the quantum manifestations of orderly and chaotic nonlinear classical dynamics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1999

Количество страниц: 386

Добавлена в каталог: 11.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
AC method      (see Askar-Cakmak method)
Action functional      160 161 162
Action integral      13 16 43 186
Action integral, under a potential barrier      148
Action variable      43 82 83 103 186 261
Action-angle variables      82 86 85 86 103—104
Action-angle variables for 1-d oscillators      232
Action-angle variables for harmonic oscillator      265
Action-angle variables for vertical pendulum      84 94
Action-angle variables, numerical method for      85 86
Adams — Bashforth four-step predictor formula      317
Adams — Moulton three-step corrector formula      317
ADI propagator      (see Altemating-direction implicit (ADI) method)
Adiabatic classical evolution      265 269 271 274
Adiabatic invariant      85 266
Adiabatic invariant, action      266 267 269 270 273
Adiabatic parameter switching of Floquet states      290 296 302 306
Adiabatic parameter switching of Floquet, time scale for      297 (Fig. 9.16)
Adiabatic perturbation theory, canonical      266
Adiabatic potential energy matrix      278 279
Adiabatic quantum evolution of Floquet states      248 251 303
Adiabatic quantum evolution, conditions for      291 294 296 297
Adiabatic quantum states      279 282
Adiabatic quantum states of pendulum      287
Adiabatic representation      (see Representation quantum adiabatic)
Adiabatic switching method      85 86
Adiabatic theorems, quantum      296
Adiabaticity parameter, classical      265
Algorithms, sources of      313 348
Altemating-direction implicit (ADI) method      336
Analytically solvable problem      10 80 87 88
Anderson localization      262
Angle variable      34 35 43 82 83 92 94 140 186 187
Anharmonic oscillator 1-d      17 114 120 144 Quartic 1-d)
Annular billiards      167
Arc length variable      76 203
Area theorem, for population inversion      291
Askar — Cakmak (AC) method      336
Atom transition operators      62
Atomic units, scaled      44
Atomic units, Table      2 1
Atomic units, unsealed      44
Autocorrelation function      52
Autocorrelation function for driven Kepler wavepacket      259
Autocorrelation function for for wavepacket in stadium      209 215
Autocorrelation function for Rydbeig atom wavepacket      53 (Fig 2.7)
Autocorrelation function for wavepacket in Henon — Heiles potential      129 130
Autocorrelation function, applications of      341 353
Autocorrelation function, calculation of      327 332
Autonomous system      5 7 157 Diamagnetic Henon-Heiles
Autonomous system, 2-d, Poincare sections for      21 23
Autonomous system, theory for      34 103 109 112 170 276
Autophasing      141
Autoresonance      268
Averaging, Baker — Campbell — Hausdorf (BCH) identity      340
Averaging, Ballistic electron motion      193 194 194 200 211 214 325 Waveguides ballistic
Averaging, Barrier      73 96 102 Tunneling
Averaging, energy quasienergy      286 287 297 299 304
Averaging, Landau — Zener model for      295
Averaging, method of      266 267
Avoided crossing(s), energy level      (see Level crossing(s))
Barrier frequency, inverted      273
Barrier height, for quartic double-well potential      97 98 99 152
Barrier penetration      145 148
Barrier penetration integral      (see Tunneling action)
Barrier penetration, application of path integral theory to      161 162
Barrier transmission, amplitude for      147
Barrier transmission, resonance in      150 151
Basis set      10 11
Basis set, coherent state      24 44 64
Basis set, diabatic      279
Basis set, Floquet state      282
Basis set, free rigid rotor      237
Basis set, harmonic oscillator      132 350 352
Basis set, Henon — Heiles      128
Basis set, hydrogen atom      45
Basis set, Kepler oscillator      261
Basis set, natural      348 350 351 352
Basis set, photon number      63
Basis set, Sturmian      349 350 351 352
Basis set, truncation of      11 352
Basis-set expansion method      10 11 341 347 348 348 350 350 353
Basis-set expansion method for bound electron wavepackets      45 48 52
Basis-set expansion method for diamagnetic Kepler problem      176 188 189
Basis-set expansion method for driven Kepler oscillator      261
Basis-set expansion method for driven Kepler wavepackets      259
Basis-set expansion method for driven particle in quantum well      225
Basis-set expansion method for driven rotor      237
Basis-set expansion method for Henon — Heiles problem      120
Basis-set expansion method for molecular dissociation      254 255
Basis-set expansion method for particle in quantum well      198 199 200
Basis-set expansion method for two-level atom, driven      68
Basis-set expansion method for wavepacket in N      2
Basis-set expansion method, level-crossing system      282
Benzophenone molecule      143 (Fig. 5.27) 144
Bias voltage on quantum well      193 194 195 196
Bias voltage on semiconductor heterostructure      210 213 221
Bifurcation(s) in diamagnetic Kepler system      180 181
Bifurcation(s) in driven Kepler system      286
Bifurcation(s) in resonant tunneling diode systems      199 200
Bifurcation(s), calculation of      325
Bifurcation(s), periodic-orbit      111
Bifurcation(s), proliferation of      137
Bifurcation(s), system without      131
Billiard system(s)      201 209 212 216
Billiard system(s), annular      167
Billiard system(s), circular      202 (Fig. 7.20)
Billiard system(s), deformed circular      204 207
Billiard system(s), elliptical      201 204
Billiard system(s), microwave cavity      201
Billiard system(s), rectangular semiconductor, array of      212 213
Billiard system(s), stadium      134 207 209 215 216
Billiard system(s), stadium, wavepacket evolution in      208 209 215
Bit-reversed data ordering      329
Bohr — Sommerfeld quantization      16 17 133 134 232
Bonds, chemical      96 115 144 273
Bonds, chemical, selective breaking of      124 125 300 301 310 311
Boundary value problem, two-point      322
Branching diagrams      325
Brillouin zone, quasienergy      230
Canonical classical perturbation theory      105
Canonical classical perturbation theory, adiabatic      266
Canonical quantum observable      87
Canonical quantum system      87
Canonical transformation(s)      76 78
Canonical transformation(s) for adiabatic theory      266
Canonical transformation(s) for nonlinear resonance approximation      141 142
Canonical transformation(s) to interaction representations      80
Canonical transformation(s), numerical representation of      86
Canonical transformation(s), successive, for superconvergent perturbation theory      106
Canonical transformation(s), time-dependent      265
Caustic      36 91 156
Caustic curve      (see Caustic)
Caustic in billiard systems      202 203 204
Caustic, effects on quantum systems      183 189 191 192 204 205 206
CCR method      (see Complex coordinate rotation method)
CH method      (see Chebyshev-expansion time)
Chaos      118 119 Lyapunov Stochastic Stochastic
Chaos in driven rigid-rotor system      236 237 259
Chaos in Henon — Heiles system      117 (Fig 5.11) 122
Chaos, global      112 176 260 261
Chaos-mediated tunneling      167
Chaotic trajectory      109 111 132 208 253
Chaotic trajectory, numerical calculation of      313 (Fig. A.l)
Characteristic exponent      225
Charge carrier, in solids      54 147 194 195
Chebyshev polynomials      342 — 343
Chebyshev — expansion time propagation (CH) method      342 — 343
Classical integrability      81 — 84 84
Classical interaction representation      79 — 81
Classical limit      39
Classical system, integrable      81 — 82
Classical system, nonintegrable      88 93 103 107 168 201 204
Classical transport, externally induced      264 — 275
Classically describable evolution      38 — 39
Classically forbidden region      145
Closed orbit theory      136 198 semiclassical)
Closed orbit theory, spectra from      187 — 189
CN differencing equation      (see Crank — Nicholson)
Coherent state      24 29 44 64
Coherent state, photon      64 — 65 65-70
Collapse of Rabi flopping      67
Collapse of Rabi flopping, time of      67
Collapse, wavepacket      46 53 259
Collocation method      338 — 339
Commuting observables, complete set of      87 — 88
Complementarity      38
Complex coordinate rotation (CCR) method      176 — 177 255 344 350-352
Complex ray method      156
Complex rotation operator      350
Complex time      162 167
Complex trajectories      162
Complexified phase space      162 163
Computer algorithms, sources of      313 348
Computer codes, parallelized      312
Computing, scientific      312 — 314
Concurrent computing, cluster of computers      312
Conductance peaks, Coulomb blockade      213 (Fig. 31) 214
Connection formulas      15 — 16 91 100 148
Constant-scaled-energy spectroscopy      178
Continuation methods      325
Continuity, equation of      2 7
Cooley — Tukey algorithm      329
Coordinate space N-dimensional (N-d)      1 4
Coordinate, tunneling      152
Coordinates for accurate finite differencing      333
Coordinates for efficient grid representations      339
Coordinates in rotating frame      171 277
Coordinates, elliptical      202
Coordinates, modified cylindrical      333
Coordinates, parabolic      88
Coordinates, semiparabolic      173 350 352
Corrector formula      317
Corrector formula, Adam — Moulton three-step      317
Correspondence for irregular quantum eigenstates      135
Correspondence, quantum-classical      5 33 37 44 46 100
Coulomb blockade regime for nanostructures      213 — 214
Coupled oscillators      114 120 142 163 164 172 176.
Coupling      11 292
Coupling to a continuum      255 372
Coupling to nanostructure leads      214
Coupling, atom-field, constant for      62 68
Coupling, between torsional modes      144
Coupling, continuum-continuum      255
Coupling, diabatic potential      279 (Fig. 9.7b) 280 282 283 284
Coupling, due to radial motion      278 — 281 282
Coupling, due to rotational motion      282
Coupling, due to tunneling      155
Coupling, electric dipole      296 (see also Dipole interaction electric)
Coupling, nonadiabatic surface hopping      346
Coupling, resonant      140
Crank — Nicholson (CN) finite difference method      334 — 335 341
Creation operator, photon      10 64
Crossing, avoided, energy — level      (see Level crossing(s))
Crossing, separatrix      (see Separatrix crossing)
Current distribution, particle mass-probability      2 13
Current — voltage characteristics of semiconductor, gate voltage      221 223
Current — voltage characteristics of semiconductor, nanostructures, bias voltage      197 199
Curvature distribution of energy levels      124
Curve crossing, potential energy      283 (Fig. 9.10a) (see also Level crossing(s) energy)
Curve, caustic      (see Caustic)
Curve, invariant      (see Invariant curve)
Danielson — Lanczos decomposition      329
Decay      38 (see also Dissociation molecular Hydrogen in ionization Resonance in
Decay of Floquet states      248 344
Decay of wavepackets      26
Decay, due to dephasing      56 (Fig. 2.9)
Decay, radiative      39 41. 59 232 301 302 303
Degree of irregularity      167
Derivative functions, of differential equations      314
Destruction operator, eigenfunction of      64
Destruction operator, photon      10
Detuning, frequency      60 63 296 298 301
Diabatic potential coupling      279 (Fig. 9.7b) 280 282 283 284
Diabatic potential energy function      279 (Fig. 9.7b) 280
Diabatic representation, molecular      277 — 281 344
Diabatic states      279 285 294
Diamagnetic interaction      171
Diamagnetic Kepler problem      111 (Fig. 5.6) 177 260 261
Diamagnetic Kepler problem and closed orbit theory      187 — 189
Diamagnetic Kepler problem, numerical treatment of      349 — 350 351-352 352-353
Diamagnetic Kepler problem, spectra of      177 — 180
Diamagnetic multiplet      174
Diatomic molecule      247 — 248 276-281 281-282 301 Rigid
Diatomic molecule, driven      234 236 249
Diatomic molecule, Landau — Zener level crossing model for      294 — 295
Differencing method, finite — difference, second order      336
Diffusion, quantum, transient      259 — 260 260-261
Dipole interaction, electric      57 61 220
Dipole moment function      300 305
Directional coupler, matter wave, four-port      211 (Fig. 7.34) 217
Discrete Fourier Transform      327 — 328
Discrete — variable spatial-grid representation, (DVR)      352 — 353
Discretization in time      335 341
Discretization of continuum states      255
Discretization of natural basis      352 — 353
Discretization of ordinary differential equations      314 — 315
Discretization of phase space      167
Discretization of wavefunctions      330 (see also Grid methods)
Dissociation by sequential frequency chirping      300 — 301 303-306
Dissociation with minimal laser pulse energy      306 — 308
Dissociation, molecular      125 254 267-269
Dissociation, selective, optimized      306 — 308 310-311
Dot, quantum      (see Quantum dot)
Double separatrix-crossing transport      271 — 275 291
Double-well potential, particle in      96 152
Double-well potential, quartic oscillator driven      165 — 167 168
Double-well potential, symmetric potential      151
Dressed state      228
Driven Kepler oscillator      43 95 233 234 255 340 in
Driven Kepler oscillator, dynamical localization in      261 — 263
Driven Kepler oscillator, Floquet states of      254 352
Driven Kepler oscillator, frequency chirped      269
Driven Kepler oscillator, ionization of      269
Driven Kepler oscillator, quantum transient diffusion in      259 — 261
Driven Kepler oscillator, separatrix crossing in      274 — 275
Driven Kepler oscillator, wavepacket evolution of      258 — 260
Driven Morse oscillator      233 (Table 8.1) 273 340 driven)
Driven Morse oscillator, dissociation of      256 — 257 300 304-306 306-308
Driven Morse oscillator, Floquet states of      251 — 254 291 292
Driven Morse oscillator, frequency chirped      267 — 269 304-306
Driven Morse oscillator, optimal control of      306 — 310
Driven Morse oscillator, pulsed      273 — 274 275 291 292
Driven Morse oscillator, separatrix crossing in      273 — 274 275
Driven particle in a infinite square well      241 — 247
Driven pendulum      233 (Table 8.1) 234
Driven planar rigid rotor      234 236
Driven quartic oscillator      165 — 167
Driven quartic oscillator, frequency swept      272 — 273
Driven quartic oscillator, pulsed and frequency chirped      294 296 344
Driven quartic oscillator, spatially open      247 — 263 (see also Diatomic)
Driven system      219 233 Driven Driven Driven Driven rotor Driven Hydrogen in
Dynamical quantum localization      261 — 263 290
Dynamical system      4 51 72 109
Dynamical system, adiabatic switching of      266 — 267
Dynamical system, driven      224 — 225
Dynamical system, parametric control of      325
Dynamical tunneling      155 156
EBK quantization      88 91 122 176
EBK quantization for regular time-periodic evolution      230 — 231
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