The semiclassical way to dynamics and spectroscopy:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
[2018]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 453 Seiten Illustrationen |
| ISBN: | 9780691163734 |
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MARC
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| 245 | 1 | 0 | |a The semiclassical way to dynamics and spectroscopy |c Eric J. Heller |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
Acknowledgments xv
Introduction xvii
PART I CLASSICAL MECHANICS WITH AN EYE TO
QUANTUM MECHANICS 1
Chapter 1 The Lagrangian and the Action 3
1.1 Extremal Action and Equations of Motion 3
1.2 Form of the Lagrangian 5
1.3 Noether s Theorem 7
1.4 Hamiltonian Formulation 10
1.5 Constrained Systems and Forces of Constraint 14
1.6 Derivatives and Legendre Transformations of the Action 16
1.7 Velocity-Dependent Potentials 19
Chapter 2 Canonical Transformations 23
2.1 Hamilton-Jacobi Idea 26
2.2 Action as the Generating Function for Dynamics 27
2.3 Phase Space and Canonical Transformations 28
2.4 Transformation of Manifolds, Areas, and Densities 30
Chapter 3 Time Evolution in Phase Space 35
3.1 Time Evolution of Point Trajectories 35
3.2 Generating Functions and Joint Probabilities 38
3.3 Poincare-Cartan Invariants 44
3.4 Poincare Surface of Section 48
3.5 Action-Angle Coordinates 50
3.6 Area-Preserving Maps 60
3.7 Poincare-Birkhoff Fixed-Point Theorem 63
3.8 Stability Analysis 66
3.9 Motion near a Periodic Orbit 71
3.10 Classical Baker s Map 74
viii Contents
Chapter 4
PART II
Chapter 5
Chapter 6
Chapter 7
Chapter 8
3.11 (Classical) Trace of a Periodic Orbit
3.12 Survival of (Most of) the Tori under Weak Interactions
3.13 Structure of Phase Space
Classical Resonance Theory
4.1 Paradigm System: Linearly Forced, Damped Oscillator
4.2 Slow External Time-Dependent Perturbations
4.3 Fast External Time-Dependent Perturbations
4.4 Averaging of Perturbations
4.5 Resonance Characteristics and Removal
4.6 Resonance and Classical Perturbation Theory
4.7 Oscillator Connection
QUANTUM AND SEMICLASSICAL MECHANICS
Aspects of Time-Dependent Quantum Mechanics
5.1 Time-Dependent Perturbation Theory
5.2 Fermi Golden Rule for Decay and Beyond
5.3 System-Bath Interactions, Dephasing, and Depopulation
5.4 Eigenstates as Fourier Transform of Dynamics
Stationary Phase Integration
6.1 One Dimension
6.2 Example: Airy Function and Linear Ramp Potential
6.3 Classically Forbidden (Tunneling) Region
6.4 Kirchhoff Method
6.5 Kirchhoff Method, Rough Surfaces, and Evanescent Waves
Feynman Path Integral to Van Vleck Propagator
7.1 Semiclassical Program
7.2 Dynamical Postulate of Quantum Dynamics
7.3 Feynman Path Integral
7.4 Van Vleck-Morette-Gutzwiller Semiclassical Propagator
7.5 Another Route to the Van Vleck-Morette-Gutzwiller Propagator
7.6 Semiclassical Energy Green Function
7.7 Trace Formula for the Energy Spectrum
7.8 Closed Orbits for Spectroscopy
7.9 History
Stressing the VVMG Propagator
8.1 Semiclassical Wavepacket Dynamics in an
Anharmonic Oscillator
8.2 Quantum and Semiclassical Revival
8.3 Autocorrelation and Spectrum in a Chaotic System
8.4 Anderson Localization
77
78
80
84
84
87
88
90
92
96
99
103
105
105
107
111
114
117
117
122
126
127
131
133
133
134
136
139
143
146
149
150
152
153
153
153
155
157
Contents
Chapter 9 Phase Space Representations of Wavefunctions
and Densities 159
9.1 Wigner Phase Space 159
9.2 Quantum Flux 162
9.3 Husimi Phase Space and Related Distributions 162
Chapter 10 Gaussian Wavepackets and Linear Dynamics 165
10.1 Phase Space Pictures of Wavepackets 169
10.2 Linear Propagators on Gaussian Wavepackets 172
10.3 Linear Dynamics Applied to More General Wavefunctions 183
Chapter 11 Gaussian Wavepacket Methods for Nonlinear
Time Evolution 185
11.1 Thawed Gaussian Approximation 185
11.2 Generalized Gaussian Wavepacket Dynamics 186
11.3 Initial Value Representation 192
11.4 Variational Wavepacket Methods 196
11.5 Wavepacket Spawning Methods 197
11.6 Maslov and Geometric Phase 198
Chapter 12 WKB Methods 199
12.1 Derivation of the WKB Wavefunction 199
12.2 Tunneling and Connection Formulas 201
12.3 WKB Through-Barrier Penetration 205
12.4 Errors and Quantum Potential 206
12.5 Quantum Reflection 207
12.6 Double Well Tunneling and Splitting 210
Chapter 13 Tunneling 214
13.1 Tunneling below and above a Barrier 214
13.2 Rigid Asymmetric Top—Showcase of Dynamical Tunneling 226
13.3 Resonance and Dynamical Tunneling in
Multidimensional Systems 230
Chapter 14 Bixon-Jortner and Fano-Anderson Models 241
14.1 Bixon-Jortner Model 241
14.2 Fano-Anderson Model 243
Chapter 15 Power of Degeneracy 246
15.1 Generator States 246
15.2 Degeneracy and Gauge Transformations 254
15.3 And the Winner Is. ... 255
PART III APPLICATIONS TO SPECTROSCOPY 257
Chapter 16 Born-Oppenheimer Approximation and Its Implications 259
16.1 Inevitability of the Born-Oppenheimer Approximation 259
16.2 Aspects of the Born-Oppenheimer Approximation 269
Contents
Chapter 17 Time-Dependent Formulations of Spectroscopy 277
17.1 Coherent Versus Single-Molecule Spectroscopy 277
17.2 First-Order Light-Matter Interaction 278
17.3 Transition Moment Operator 278
17.4 Time Correlation Constraints on the Frequency Spectrum
and Vice Versa 284
17.5 C.W. Spectroscopy from the Molecule s Point of View 288
17.6 Spectroscopy at Finite Temperature 291
17.7 Photoelectron Spectroscopy 291
17.8 Second-Order Light-Matter
Interaction—Raman Spectroscopy 294
17.9 Raman Amplitude 296
17.10 Raman Amplitudes from the Tme Domain 296
17.11 Raman Scattering for a Few Degrees of Freedom 298
17.12 Raman Wavefunction 298
17.13 Complete Raman Emission Spectrum 300
17.14 Raman Scattering for Many Degrees of Freedom 301
Chapter 18 Semiclassical Spectroscopy 303
18.1 Semiclassical Franck-Condon Factors 303
18.2 Classically Forbidden Franck-Condon Factors 307
Chapter 19 Semiclassical Dynamics and One-Photon Spectroscopy 313
19.1 Pseudo or MIME Modes in Spectra 314
19.2 Photodissociation of a Molecule 318
19.3 Benzophenone: Transition from Stable to Unstable Motion 322
19.4 Serendipity—the Toy Spectrum Is Real 331
19.5 Recapitulation 333
Chapter 20 Semiclassical Dynamics and Two-Photon Spectroscopy:
Raman Scattering 336
PART IV CHAOS AND QUANTUM MECHANICS 341
Chapter 21 Aspects of Quantum Chaology 343
21.1 Semiclassical Tmeline 344
21.2 Anticipating the Stages of Evolution in a Chaotic System . 345
21.3 Understanding Quantum Ergodicity 348
21.4 Measures of Ergodicity in Quantum
(and Classical) Mechanics 351
21.5 Time Development of Dynamical Constraints 355
21.6 Random Spectra and Quantum Ergodicity 357
21.7 Propynol 364
21.8 Rate of Exploration of Phase Space 369
21.9 The Rate of Exploration 7Z 371
381
383
387
388
389
390
394
395
397
397
406
408
408
409
410
412
413
415
416
418
422
424
425
431
433
433
434
437
439
449
Quantum Scars of Classical Periodic Orbits
Random Waves and Nodal Structure of Eigenstates
23.1 Random Waves
23.2 Intersection of Nodal Surfaces and Role of
Evanescent Waves
23.3 Fermionic Wavefunctions
23.4 Classically Forbidden Regions in Few-Body Eigenstates
23.5 Where Does Tunneling Start in Many Dimensions?
23.6 Many-Particle Random Waves and Statistical Mechanics
23.7 Diagonal Limit
23.8 Link to the Canonical Ensemble
Branched Flow
24.1 Classical Branched Flow
24.2 Wave Branched Flow
Decoherence
25.1 Calculating the Density Matrix
25.2 Coherence in Photoemission
25.3 Decoherence in a Collision with a Bath Particle
25.4 Diffraction and Interference of Buckyballs
25.5 Split Beam Coherence
25.6 Sticking or No Sticking?
25.7 Semiclassical Wavepacket Approaches to Decoherence
Multiple Scattering Theory
26.1 Point Scatterer Model
26.2 Walls as Point Arrays
26.3 Quantum Corrals
26.4 Fermi Pseudopotential
Appendix
A.1 Partial Derivative Identities
A.2 Gaussian Integrals
Further Reading
Bibliography
Index
|
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| author_facet | Heller, Eric J. 1946- |
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| author_sort | Heller, Eric J. 1946- |
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| building | Verbundindex |
| bvnumber | BV045461974 |
| classification_rvk | UK 1000 |
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| ctrlnum | (OCoLC)1061241823 (DE-599)BSZ507258290 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV045461974 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:18:42Z |
| institution | BVB |
| isbn | 9780691163734 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030847213 |
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| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-20 DE-83 |
| physical | xviii, 453 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Princeton University Press |
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| spelling | Heller, Eric J. 1946- Verfasser (DE-588)103209155X aut The semiclassical way to dynamics and spectroscopy Eric J. Heller Princeton ; Oxford Princeton University Press [2018] xviii, 453 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quasiklassisches Modell (DE-588)4318601-4 gnd rswk-swf Quasiklassisches Modell (DE-588)4318601-4 s DE-604 Quantenmechanik (DE-588)4047989-4 s Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030847213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heller, Eric J. 1946- The semiclassical way to dynamics and spectroscopy Quantenmechanik (DE-588)4047989-4 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4318601-4 |
| title | The semiclassical way to dynamics and spectroscopy |
| title_auth | The semiclassical way to dynamics and spectroscopy |
| title_exact_search | The semiclassical way to dynamics and spectroscopy |
| title_full | The semiclassical way to dynamics and spectroscopy Eric J. Heller |
| title_fullStr | The semiclassical way to dynamics and spectroscopy Eric J. Heller |
| title_full_unstemmed | The semiclassical way to dynamics and spectroscopy Eric J. Heller |
| title_short | The semiclassical way to dynamics and spectroscopy |
| title_sort | the semiclassical way to dynamics and spectroscopy |
| topic | Quantenmechanik (DE-588)4047989-4 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd |
| topic_facet | Quantenmechanik Quasiklassisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030847213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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