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