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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 |
Quantum-classical comparisons, Planck’s constant, dimensionless 19
Quantum-classical comparisons, two, coupled 165
Quasieneigy 165 225
Quasieneigy for driven two-level system 228
Quasieneigy, avoided crossings of 286 — 287 295 297 299 304
Quasieneigy, Brillouin zones of 230
Quasieneigy, doublet splittings 167 168
Quasieneigy, EBK quantization of 230 — 231
Quasieneigy, examples of 243 (Fig. 8.16) 297 9 304
Quasieneigy, operator 227
Quasieneigy, shells of 230
Quasiperiodic orbit 34 — 35 123
Quasiprobability function, photon (see Q — function phase
Rabi flopping (see Rabi oscillations)
Rabi flopping frequency 60 67 228
Rabi frequency 60 66 298
Rabi frequency, n-photon 63
Rabi oscillations 57 — 60 299
Radial coupling 282
Radial momentum matrix, adiabatic 278 279 280
Raman scattering, stimulated 303
Random matrix theory of spectral fluctuations 288 — 290
Rectangular billiards cavities, array of 212 — 213
Recurrence spectroscopy, see Spectrum, recurrence strengt 382
Recurrences, in wavepacket evolution 283 — 285
Reference trajectories 28 50 75 107-108 209
Reference trajectories, chaotic 109 111 132
Reference trajectories, difference function 74
Reference trajectories, heteroclinic and homoclinic 113
Reference trajectories, orbitally stable (see Orbital stability of
Reference trajectories, regular and irregular 109
Regular evolution, wavepacket 129 130
Regular quantum eigenstate (see Energy)
Representation, classical, interaction 79 — 81
Representation, classical, spatial 76 — 77
Representation, Heisenberg 3
Representation, initial-value 191 — 192
Representation, interaction 81 256
Representation, molecular (see Molecular representation)
Representation, phase space 23 — 24 31-34 184 189 341
Representation, quantum, adiabatic 277 — 281
Representation, quantum, diabatic, good 281
Representation, Schroedmger 3 25 89
Representation, spatial-grid, numerical 332 — 334 338-339 352-353
Representation, standard diabatic 277
Representation, switching during timesteps 326
Residue 76 131
Resonance phase difference 141
Resonance state in continuum 350
Resonance state, nonlinear (see Nonlinear resonance quantum)
Resonance — island trapping (see Nonlinear resonance trapping)
Resonance — mediated tunneling (see Tunneling resonance
Resonance, classical 139 (see also Nonlinear resonance)
Resonant action vector 139
Resonant tunneling diode (see Tunneling diode resonant
Revival ill driven Kepler system 259
Revival in hydrogen atom 46 — 50 53
Revival in stadium billiards 209
Revival of Rabi flopping 67
Revival, fractional 46 48 50
Revival, time of 46
Revival, wavcpacket 46 — 50 99
Richardson extrapolation 334
Rigid rotor, driven 234. 236 — 241
Rigid rotor, planar free 234
Rotating wave approximation (RWA) 58 — 59
Rotating wave approximation (RWA) for Floquet states 227 — 228
Rotating wave approximation (RWA), applications of 291 — 294 295 297
Rotating wave approximation (RWA), strong-field breakdown of 68 — 69
Rotation angle 176 255 350
Rotation operator, complex 350
Rotational coupling 277 282
Rotor, rigid (see Rigid rotor)
RTD (see Tunneling diode resonant
Runge — Kutta 315 — 316
Runge — Kutta method 315 — 316
Runge — Kutta method, fourth-order 316
Runge — Kutta method, second-order, optimal 316
RWA (see Rotating wave approximation (RWA))
Rydberg atom 44 48
Rydberg atom, experiments with 48 — 49 60 61 experiments
Scaled semiparabolic coordinates 173
Scaling 7 — 8 97-98 131 132
Scaling for diamagnetic Kepler system 171 — 172 173
Scaling of action variables 232
Scaling of atomic units 44 248 249
Scaling of energy 131 172
Scaling of energy density of states 187 — 188
Scaling of Hamiltonians 8 116 131
Scaling of Planck’s constant 14 98 132 237
Scaling of time, for adiabatic evolution 265 270
Scarred quantum eigenstate (see Energy)
Schrodinger equation for electronic states of diatomic molecules 281
Schrodinger equation for Floquet states 225
Schrodinger equation, phase-space 31 33
Schrodinger equation, time-dependent 2
Schrodinger equation, time-independent 3 10 161
Scientific computing 312 — 314
Second-order midpoint method 315
Selective breaking of chemical bonds 124 — 125 300-301 310-311
Semiclassical evolution 39 50 189-193 209
Semiclassical propagator (see Propagator theoretical semiclassical)
Semiclassical quantization (see EBK quantization)
Semiconductor, devices, ballistic evolution in (see Ballistic electron motion)
Semiconductor, heterostructures (see Heterostructures lateral semiconductor)
Semiconductor, nanostructure (see Nanostructure semiconductor)
Semiconductor, quantum well (see Quantum well)
Semiconductor, tunneling diode (see Tunneling diode)
Semiparabolic coordinates 173 350 352
Sensitivity analysis, of energy eigenvalues 3 — 124 125
Separable equation 82 84 87 88
Separatrix 36 — 37 73 174 232 270
Separatrix crossing 85 270
Separatrix crossing, double, transport due to 271 — 275 291
Separatrix crossing, quantum 99 100 274
Separatrix eigenstate, quantum 95 — 96 101 102 174
Separatrix, broken 209
Separatrix, dynamics near 271
Separatrix, evolution on 74
Sequential frequency chirping, molecular, dissociation by 300 — 301 303-306
Shannon entropy 239 — 240
Shooting methods for ordinary differential, equations 322 — 324 347-348
Shooting methods for ordinary differential, multiple shooting 323
Short iterative Lanczos (SIL) method 331
Sideband index 219
SIL method (see Short iterative Lanczos method)
Sinusoidally driven Kepler problem (see Hydrogen atom(s) in Driven
Slowness parameter 265 270
Snapshots of ensemble evolution, stroboscopic 7 238 267
Software 312 — 313
Software for barrier problems 147
Software for wavepacket evolutio 28. 342
Software, FFT 329
Software, matrix diagonalization 348
Software, message-passing 312
Software, shooting method 347
Solitary wave 286
Soliton 286
SPA (see Stationary — phase approximation)
Spatial grid 330
Spatial — grid method (see Grid methods numerical)
Spatial — grid representation, discrete — variable (see Discrete-variable spatial-grid representation (DVR))
Spatial — grid representation, Fourier, global 338 — 339
Spatially-bounded system 232
Spatially-open system 232
Spectral analysis 325 — 327 (see also Discrete)
Spectral determinant 186
Spectral fluctuations, random matrix theory of 288 — 290
Spectral function 25
Spectral method 337
| Spectroscopy, constant-scaled-eneigy 178 180
Spectrum, clustered 143 (Fig. 5.27) 144 176
Spectrum, complex rotated 176 — 177 351
Spectrum, diamagnetic Kepler 178 — 180 187-189
Spectrum, laser fluorescence 143 (Fig. 5.27)
Spectrum, molecular, tunnel doublets 151 — 152
Spectrum, photoabsorption 178 — 180
Spectrum, photoluminescence 55 (Fig. 2.8)
Spectrum, quasieneigy 243 (Fig. 8.16)
Spectrum, recombination line 194 — 196
Spectrum, recurrence-strength 178 188 190 199 200
Spectrum, sideband 221 (Fig. 8.2) 223 230
Spin-boson model 346
Spins, driven collection of 287
Split — operator (SPO) methods in phase space 341
Split — operator (SPO) methods, numerical 9 — 342 344 346
Split — operator (SPO) methods, polynomial propagator 344 — 345
Splittings, quasieneigy doublet 167 168
SPO FFT grid 283 339
SPO method 342
SPO methods (see Split — operator (SPO) methods numerical)
SPO polynomial-propagator 344 — 345
SPO polynomial-propagator, stability of 331 (Table B.l)
SPO wavepacket calculations 341 343
Square well, infinite, driven particle in 241 — 247
Stability analysis 22 71 Orbital Residue)
Stability matrix 72 — 74 185 187 191
Stabilization against ionization, classical and quantum regions of 251
Stable fixed point (see Fixed point stable)
Stable manifold(s) (see Manifold(s))
Stable periodic orbit (see Periodic orbit stable)
Stadium billiards 134 207 215-216
State — vector model for time-dependent two-state, system 299 — 300
State, quantum (see Energy eigenstate(s) quantum)
State-mixing parameter, slowly varying 292
Stationary phase 140
Stationary state(s) 3 10 15 93 132-133 quantum)
Stationary state(s), numerical calculation of 347 — 353
Stationary-phase approximation (SPA) 136 149 160 162 183 185
Stationary-phase approximation (SPA), within function space 161 162
Statistics, energy level 287 — 290
Step potential 1 — d 32-33 54
Stepsize, in time, numerical 81 318
Stepsize, in time, numerical, adaptive control of 316
Stiff sets of ordinary differential equations 318 — 319
Stimulated Raman scattering 303
Stochastic layer 85 111
Stochastic layer and chaos-mediated tunneling 164 167 168 9
Stochastic layer and irregular quantum states 122 252
Stochastic layer and quantum transient diffusion 260
Stochastic layer, eigenstate overlap with 167 168
Stochastic layer, examples of 204 205 237 241 242
Stochastic web 112 113 326
Stokes laser pulse 303
Stroboscopic Poincare section (see Poincare section stroboscopic)
Stroboscopic snapshots 237 238 267
Stumiian states 255 349 351-352
Sturmian functions, spherical 349
Superconvergent perturbation theory 106
Surface of section 22 31 35
Surface-state electron problem 234
Survival probability 259 (see also Autocorrelation function)
Swallow tail state 206 (Fig. 7.25)
Switching method, adiabatic 85 — 86
Symmetric double — well potential (see Double well potential particle
Symplectic 75
Symplectic matrix 75
Three-level systems 301 (Fig. 9.20)
Three-point spatial differencing 333 — 334 335 337
Time correlation, of two functions 327
Time propagator (see Propagator)
Toda lattice problem 81 — 82
Torus in phase space, N — dimensional (N — D) 36 84 104 112 163 164
Torus in phase space, quantization of 88 92
Trace formula 185 — 187 290
Trajectory (see Chaotic trajectory; Orbit)
Trajectory in phase space (see Phase — space trajectory)
Trajectory, nuclear separation 282
Trajectory, propagation of (see Hamilton’s equations numerical
Trajectory, reference (see Reference trajectories)
Trajectory, separatrix (see Separatrix)
Transformation, canonical (see Canonical)
Transient diffusion, quantum 259 — 260 260-261
Transition operator, atom 62
Transmission resonance, barrier 150 — 151
Transmission resonance, double barrier 150 — 151 196
Transmission resonance, through quantum dots 221 223
Transport, quantum (see also Ballistic electron)
Trapping, nonlinear resonance (see Nonlinear)
Trotter product formula 158 340
Tunnel doublet 151 — 152 167 168
Tunneling 102 144
Tunneling action 148 151
Tunneling coordinate 152
Tunneling delay time 149 — 150
tunneling diode 194 — 200
Tunneling diode, resonant (RTD) 196 — 200
Tunneling frequency 155
Tunneling in phase space 164 — 169
Tunneling splitting, energy-level 152 — 154
Tunneling time 149 — 150
Tunneling, chaos-mediated 164 167
Tunneling, dynamical 155 156 164
Tunneling, microwave modulation of 221 — 224
Tunneling, multidimensional 156 157 163
Tunneling, path integral theory of 161 — 163
Tunneling, photon assisted 223
Tunneling, resonance-mediated 164 168
Tunneling, steady 145 — 148
Tunneling, through heterostructure barriers 149 — 150 194
Tunneling, wavepacket 149 — 151
Turning point 12 15 17 42 98 147 148. 285
Turning surface (see Caustic)
Turnstile 209
Two-level system(s) (driven) 57 — 60 111 227-228
Two-level system(s) (driven), pulsed 290 — 294 295
Two-level system(s) (driven), pulsed and frequency chirped 296 — 300
Two-level system(s) (driven), second quantized 61 — 63 64-69
Two-point boundary value problem 322
Unstable equilibrium, point of 36 — 37 97. unstable)
Unstable fixed point (see Fixed point unstable)
Unstable manifold(s) (see Manifold(s))
Unstable periodic orbit (see Periodic orbit unstable)
Variational method 306 307
Vector 2
Vector, frequency, classical 39 83 105.
Vector, nuclear separation 276
Vector, polarization 61
Vector, resonant action 139 141
Vector, Runge — Lenz 174
Vector, state-, quantum 299
Velocity function, phase-space 4
Velocity, probability flow, in coordinate space 13
Vortex tube 231 242 252 253
wavefunction (see also Energv eigenstate(s) quantum)
Wavefunction, discretized 300
Waveguide, ballistic electron 210 (Fig. 7.29) 211 217
wavepacket 25 — 26 (see also Wavepacket evolution)
Wavepacket collapse 46 49 53
Wavepacket evolution 125 — 126
Wavepacket of molecular nuclear coordinate(s) 282 — 285 345
Wavepacket propagation, semiclassical reference — trajectory method for 50 — 53 209
Wavepacket recurrences 283 — 285
Wavepacket revival 46 — 50 209
Wavepacket revival, fractional 48 (Fig. 2.4) 50 53
Wavepacket, bound electron 44 — 53
Wavepacket, complex 126 — 128
Wavepacket, driven Kepler 258 — 260
Wavepacket, free particle 25 — 27
Wavepacket, irregular 129 — 130 189 259
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