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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Bayfield J.E. — Quantum Evolution: An Introduction to Time-Dependent Quantum Mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Eccentric anomaly angle 42 43
Effective charge 54
effective mass 54 147 241
Ehrenfest’s theorem 3
Eigenstate (see Energy eigenstate(s) quantum)
Eikonal ansatz 12
Eikonal theory 11 — 13 89-90 91
Einstein — Brillouin — Keller quantization (see EBK quantization)
Electromagnetic cavity, mode of 61 64 65
Electromagnetic field, monochromatic classical 8 — 9
Electromagnetic field, second quantization of 9 — 10
Electron gas 194 196 210 212
Electron wavepacket 41 44 258-260
Electronic basis functions, adiabatic molecular 282
Elliptic fixed point 73 (see also Fixed point stable)
Elliptical billiards (see Billiard system(s) elliptical)
Energy density of states 136 — 137 184 185 187 197 197-199 200
Energy density of states, diamagnetic Kepler 187 — 188 189
Energy eigenstate(s) from wavepacket evolution 192 (Fig. 7.12) 193 209
Energy eigenstate(s), basis — set calculation of (see Basis-set expansion method)
Energy eigenstate(s), billiard 201 203 208
Energy eigenstate(s), diamagnetic Kepler 176
Energy eigenstate(s), electromagnetic field (see Photon — number eigenstate)
Energy eigenstate(s), harmonic oscillator 27
Energy eigenstate(s), Henon — Heiles 123 (Fig. 5.15) 124 128
Energy eigenstate(s), hydrogen atom 45
Energy eigenstate(s), irregular 122 124 135 176 204
Energy eigenstate(s), KAM (see KAM quantum state(s))
Energy eigenstate(s), modulated (see Modulation of quantum states external)
Energy eigenstate(s), overlap with stochastic layer 167 168
Energy eigenstate(s), pendulum 93 — 94
Energy eigenstate(s), quantum 3 10
Energy eigenstate(s), regular 123 (Fig. 5.15) 163 164 KAM Nonlinear quantum)
Energy eigenstate(s), scarred 130 — 131 133-134 176 189 192 204 208 216 245-247
Energy eigenstate(s), semiclassical 88 100
Energy eigenstate(s), shooting method for 347 — 348
Energy eigenstate(s), WKB separatrix 93 94 95 101 102 174
Energy eigenvalues (see Basis — set expansion)
Energy eigenvalues method (EBK quantization)
Energy levels of trajectories 24 32 33 209 237 238 240 251 260 261 269
Energy levels, clusters of 143 (Fig. 5.27) 144 176
Energy levels, crossing of (see Level crossing(s))
Energy levels, curvature distribution of 124
Energy levels, displaced differences of 39 — 40
Energy levels, Henon — Heiles 121 (Fig. 5.14)
Energy levels, ladders of (see Ladders of energy levels)
Energy levels, number density of 136 — 137 (see also Energy density of states)
Energy levels, quantum, bands of 53
Energy levels, quantum, spacings of 232 287 289
Energy levels, quantum, statistics of 287 — 290
Energy levels, semiclassical 92 100
Energy levels, sensitivity analysis of 123 — 124 125
Ensemble of initial conditions (see Initial conditions)
Entropy, Shannon 239 — 240
Equilibrium point 72. See also Fixed point
Essentially quantum eigenstates 165 288
Essentially quantum system 38 — 39 87 145
Euler differential equations 307
Euler's method 315
Exciton 54 56 57
Exponentiation, rate of 74 100
Extended phase space 7 226
External nonlinear resonance (see Nonlinear resonance external)
F2-type 82 89 105
Fast Fourier transform (FFT) 328 — 329
FFT (see Fast Fourier transform)
FFT for energies and eigenfunctions 353
FFT for Floquet states 344
FFT grid method (see Grid methods numerical)
FFT, finite-differencing 150
FFT, split-operator (SPO) 32 283 305 310 339 344 346 353
Field modulation (see Modulation of quantum)
Finite difference calculation 150 (see also Finite)
Finite difference method for numerical quantum evolution 332 — 337
Finite difference method for periodic orbits 325
Finite difference method, Askar — Cakmak (AC) 336
Finite difference method, Crank — Nicholson (C’N) 334 — 335
Finite difference method, Peaceman — Rachford (PR) 336 — 337
Finite — difference second-order differencing, method 336
First return map (see Poincare map)
Fixed point 35 72
Fixed point, stable 23 (Fig. 1.8) 72 129 166 175
Fixed point, unstable 37 73. 100 112 115 166 174 245
Fj-type 265
Floquet 238 — 240 253 254
Floquet operator (see Floquet propagator)
Floquet picture of 228
Floquet picture of in regular driven wavepacket evolution 259
Floquet picture of microwave two-photon 61 (Fig. 2.11)
Floquet picture of two-level system in coherent field 66 — 67 69
Floquet propagator 224 226 229 344
Floquet state 229
Floquet state of propagator 190 — 192
Floquet state(s) 165 225 227 229
Floquet state(s) for driven Kepler problem 249 250 352
Floquet state(s) for driven Morse oscillator 251 — 254
Floquet state(s) for driven particle in an infinite square well 241 — 247
Floquet state(s) for driven rotor 237 — 241
Floquet state(s) for driven two-level system 227 — 228
Floquet state(s), adiabatic evolution of 303
Floquet state(s), adiabatic parameter switching of 290 — 296
Floquet state(s), extended 238 239 240
Floquet state(s), irregular 239 — 241 246 253
Floquet state(s), mean energy of 230
Floquet state(s), nonlinear resonance, external 234 — 236
Floquet state(s), numerical computation of 344 352
Floquet state(s), regular 246 (Fig. 8.18a) 253
Floquet state(s), scarred 245 — 247 251-252 253
Floquet state(s), types of 254
Floquet state, nonadiabatic surface-hopping 346
Floquet state, random 288
Floquet state, rotational coupling 282
Floquet theory 165 224 228 264
Floquet’s theorem 224
Flow velocity (see Probability flow velocity)
FORTRAN codes 313
Fortran codes, double-precision 314
Fortran codes, optimization of 313
Forward bias voltage 193 194
Fourier series 105 140 327
Fourier series, applications of 219 224 230 235
Fourier spatial-grid representation 338 — 339
Fourier transform 25 29 91 326 327 337
Fourier transform of 214 215 369 370
Fourier transform of wavepacket autocorrelation function 215
Fourier transform, applications of 178 188 189 193 212
Fourier transform, computation of 326
Fourier transform, discrete 327 — 328
Fourier transform, fast 328 — 329
Fourier, global 344
Fractional revivals, wavepacket 46 48 50
Franck — Condon transition 283 308
Free particle 12 25 80 201
Free particle in time-periodic electric field 229
Frequency chirping, laser, induced processes by 5 — 266 267-270 296-306 308 9 310
Frequency detuning 60 63 296 298 301
Frequency vector, classical 39 83 105 107
Function space 159 — 160 161
Function space integral 160
Function space integral for Huisimi distributions 29
Function space integral for Kepler wavepacket evolution 45 — 46 47 48 2.4) 51
Function space integral for particle 1-d quartic oscillator potential 99 100
Function space integral, dynamical tunneling of 155
Function space integral, Gaussian wavepacket 25 — 28 (see also Wavepacket)
Function space integral, incident 1-d rectangular barrier 150 151 342
Function space integral, INDE 375
Functional 306
Functional, action 160 161 162
Functional, minimization of 306 307 309
Gaussian wavepacket dynamics (GWD) algorithm 346
| Gaussian wavepacket dynamics — path integral (GWD — PI) method 345 — 347
Gaussian wavepacket dynamics, global 332
Gaussian wavepacket dynamics, Lanczos 330 332
Gaussian wavepacket dynamics, monodromy matrix 323 — 325
Gaussian wavepacket dynamics, multistep 316 — 318
Gaussian wavepacket dynamics, short iterative (SIL) 331 (Table B.1) 332
Generalized n-pulse 291
Generating function 77 78
Global chaos 112 176 260
Global numerical propagation methods 332 342
Gradient dyadic, Hamiltonian (VZVZH) 75 109
Gram — Schmidt reorthonormalization 320 — 321
Green’s function for the Schrodinger equation 157 162 183 184 209
GSR (see Gram — Schmidt reorthonormalization)
GWD (see Gaussian wavepacket dynamics)
GWD — PI method 345 — 347
Hamilton — Jacobi equation 13 78 82 162
Hamiltonian 7 — 9
Hamiltonian flow 5 — 7
Hamiltonian for driven particle in square well 241
Hamiltonian for driven quartic oscillator 166 (Fig. 6.6)
Hamiltonian for driven rigid rotor 234
Hamiltonian for driven systems 233 (Table 8.1)
Hamiltonian for driven two-level system 62 63
Hamiltonian for free particle in oscillating field 229
Hamiltonian for frequency-chirped harmonic oscillator 265
Hamiltonian for frequency-chirped quartic oscillator 272
Hamiltonian for quantum well in magnetic field 197
Hamiltonian matrix, diagonalization of 10 — 11 19 132
Hamiltonian matrix, direct 348 — 350
Hamiltonian system, integrable 82 103
Hamiltonian, complex rotated 255 350
Hamiltonian, diamagnetic Kepler 171 173
Hamiltonian, diatomic molecule 276
Hamiltonian, extended 226
Hamiltonian, frozen 265
Hamilton’s characteristic function 79
Hamilton’s equations 4 — 5 51 75
Hamilton’s equations for an interaction Hamiltonian 80
Hamilton’s equations for the pendulum 36
Hamilton’s equations in action-angle variables 83 139
Hamilton’s equations, extended 226 265
Hamilton’s equations, numerical iteration of 314 318 319 321
Hamilton’s principal function 13 78 80
Harmonic oscillator(s) 8 9 27 54 80
Harmonic oscillator(s), basis sets 19 27 120 132 350 352
Harmonic oscillator(s), frequency chirped 265 — 266
Harmonic oscillator(s), quantum 9 — 10 17 24 27-28 51
Harmonic oscillator(s), two, coupled 114 120 163 164 172
Heisenberg representation 6 — 7
Henon — Heiles 114 115 116 120
Henon — Heiles problem 22 81 114
Henon — Heiles problem, energy-level diagram for 121 (Fig. 5.14)
Henon — Heiles problem, quantum 119 — 130
Henon — Heiles problem, regular energy eigenstate 122
Henon — Heiles problem, wavepacket evolution in 126 — 130
Henon — Heiles, interaction 61 79 139
Henon — Heiles, nonautonomous 7
Henon — Heiles, quartic oscillator 96 97 152
Henon — Heiles, scaled 8 14 116
Herring’s formula 154
Heteroclinic trajectory 113
Heterostructures, lateral, biased 194 — 200 210 221-223
Heterostructures, lateral, nanostructures embedded in 210 — 214
Heterostructures, lateral, numerical design of 343 348
Heterostructures, lateral, semiconductor 55 147 194
Heterostructures, lateral, tunneling in 147 149 194-196
Holes, in semiconducting materials 54
Homoclinic trajectory 113 114
Householder algorithm 348
Huisimi distribution function 29 — 30 99 167 242-247
Hydrogen atom(s) 11 30 41 44 77 92 247 339
Hydrogen atom(s) in laser field 337
Hydrogen atom(s) in microwaves 248 — 251 261-262 263 340 352
Hydrogen atom(s) in static electric field 84 376
Hydrogen atom(s) in static magnetic field (see Diamagnetic Kepler problem)
Hydrogen atom(s), basis sets 45 349
Hydrogen atom(s), classical orbits of 41
Hydrogen atom(s), complex coordinate rotation calculations 350 — 352
Hydrogen atom(s), experiments with 177 — 180 220-221 248-251
Hydrogen atom(s), field-modulated 220 — 221
Hydrogen atom(s), finite differencing for 332 — 333
Hydrogen atom(s), generalized coherent states 83
Hydrogen atom(s), Huisimi distribution function 29 — 30
Hydrogen atom(s), ionization of 249 — 251
Hydrogen atom(s), pulsed 248 249 274-275
Hydrogen atom(s), wavepacket evolution 44 — 46 47 48 2.4) 51
Imaginary-time techniques 137 — 138
Implicit differencing 319
Implicit differencing, Maslov 19 92 183 185
Implicit differencing, Mathieu 94 96 242 243
Implicit differencing, Morse 183
Implicit differencing, other 191
Implicit differencing, sideband 219
Infinite square-well potential, driven particle in 220 241
Initial conditions, ensembles of, in phase space 24
Initial conditions, sensitivity to 319 (see also Lyapunov exponents Orbital
Initial value problem 314 322 330
Instanton method 167
Integrable system, classical 81 — 82 84 109 202
Interaction Hamiltonian 61 79 139
Interaction representation, classical 79 — 81
Interaction representation, quantum 256
Internal nonlinear resonance (see Nonlinear resonance internal)
Invariant curve 21 — 22 36 203
Inversion, field 252 254 256
Inversion, population (see Population inversion)
Ionization, microwave (see Hydrogen atom(s) in ionization
Irregular evolution, classical 109 — 111 118-119 263
Irregular evolution, wavepacket 129 — 130 189-193 208-209 259
Irregular quantum energy eigenstate(s) (see Energy eigenstate(s) quantum irregular)
Irregular quantum systems 170 171
Irregular quantum systems, semiclassical theory for 136 — 138 182-186
Irregularity, measures of 119 (Fig 5.13) 167 176
Jacobian 72
Jacobian, monodromy (see Monodromy matrix)
Jacobian, Poisson 10
Jacobian, random 288 — 290
Jacobian, stability (see Stability matrix)
Jaynes — Cummings model (JCM) 62 — 63
Jaynes — Cummings model (JCM), collapse and revivals in 66 — 67
Jaynes — Cummings model (JCM), Q-function for 65 — 66
JCM (see Jaynes — Cummings model)
Josephson junction 234
KAM quantum state(s) 122 176
KAM systems 103 — 107 113-114 164 187 236
Kam theorem 105 — 107
KAM tori 104 112 114 204
Kepler oscillator 1 — d, driven (see Driven Kepler oscillator)
Kepler problem (see Hydrogen atom(s))
Kepler problem, diamagnetic (see Diamagnetic Kepler problem)
Ladders of energy levels 247 (Fig. 8.19)
Ladders of energy levels for Henon — Heiles system 121 (Fig. 5.14) 128
Ladders of energy levels, vibrational, for diatomic molecules 247 283 303 305
Lagrange multipliers 307 324
Lagrangian surface 183
Lanczos algorithm 330 332
Lanczos method, short iterative 331 (Table B.l) 343 344
Landau — Zener (LZ) model 281 294
Landau — Zener parameter for atom-atom collision 295
Landau — Zener parameter for field-switched two-level system 295
Langer modified potentials 19 20
Laser excitation 48 — 49 54-56 124 177-180 283 302-306
Laser excitation, dynamics initiated by 48 — 49 56
Laser excitation, fluorescence spectrum 143 (Fig. 5.27)
Laser excitation, photoabsorption spectra 178 — 180 188 190
Laser excitation, photoionization signals 49 (Fig. 2.5) 302
Laser excitation, spectroscopy 55 143 144 220
Laser pump-probe experiment 49 55
Laser-driven dynamics 256 — 257 303-306 308 309 310
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