Table of contents for Introduction to quantum mechanics : a time-dependent perspective / David J. Tannor.


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PART I         Pictures and Concepts        I
CHAPTER I      The Time-Dependent Schr6dinger Equation     3
1.. 1 Separation of Variables and Reconstitution of the Wavepacket 4
1.2 Expectation Values 5
1.3 A Worked Example: Particle in Half a Box 7
Further Reading and Historical Notes 10
References 11
CHAPTER 2      The Free-Particle Wavepacket   13
2A1 General Solution 13
2.2 The Center of the Wavepacket 16
23  The Dispersion of the Wavepacket Ji
Problems 20
Further Reading and Historical Notes 21
References 21
HAPTER 3      The Ga ussian Wavepacket   23
3.   The Gaussian Free Particle  23
3.2 General Properties of Gaussian Wavepackets 26
3,3 Gaussian in a Quadratic Potential 28
3.4 Reexamination of the Stationary Phase Method  31
Problems 33
References 34
HAPTER 4      Correspondence between Classical and Quantum Dynamics       35
4.1 Ehrenfest's Theorem  35
4.2 jBohmian Mechanics and the Classical Limit 38
4.3 Fractional Revivals 46
Problems 49
References 53
CHAPTER 5     The Wigner Representation and the Density Operator     55
51 The Concept of Phase Space  56
5.2 The Wigner Representation of Wavepackets 58
53  The Density Operator 61
5.4 Wigner Representation of the Density Operator 68
Problems 74
References 76
CHAPTER 6     Correlation Functions and Spectra   81
61 Spectra as Fourier Transforms of Wavepacket Correlation Functions  I
6.2 General Properties of Fourier Transforms 86
6E3 ig enfunctions as Fourier Transforms of Wavepackets 97
Problems  103
References 108
CHAPTER 7     One-Dimensional Barrier Scattering    109
7.1 Wavepacket Formulation of Reflection and Transiission
Coefficients  110
7.2 Cross-Correlation Function Formiulation of Barrier Scattering and the
S-Matrix  116
73  Scattering Theory Using Eigenstates  122
T4   Overlap Integrals of Scattering EIgenstates  128
7.5 Reconstituting the Wavepacket firom the Scattering Eigenstates  132
7.6 Resonances and Time Delay  134
Problems 138
References 140
PART 11       Formal Theory and Methods of Approximation               141
CHAPTER 8      Linear Algebra and Quantum Mechanics     143
8.1 Linear Vector Spaces  143
K2 Operators: Mapping a Wavefunction to Another Wavefunction 147
8.3 Discrete Basis Sets: The Bridge between Operators-Wavefunctions
^   Matrices-Vectrs  159
84 Continuous Basis Sets  172
Problems 179
References 183
CHAPTER 9     Approximate Solutions of the Time-Dependent
Schr6dinger Equation   185
9.1 'The Schr6dinger, Heisenberg and Interaction Pictures  186
9.2 Time-Dependert, Perturbation Theory 190
9.3 The Magnus Expansion and Wei-Norman Factorization 193
9.4 Adiabatic Dynamics and the Geometrical Phase  199
9.5 Periodic Hanfiltonians and Floquet Theory  208
9-6 Variational Principles and the Time-Dependent Self-Consistent Field
Approximation 214
Problems 220
References 222
CHAPTER 10    Path Integration, the van VIeck Propagator and
Semiclassical Mechanics 227
101 The Classical Action 228
10.2 Path Integration 238
10.3 The van VIeck Propagator 240
10.4 The Propagator as a Unitary Transformation  246
10.5 Gaussian Wavepackets and the van VIeck Propagator 257
References 268
CHAPER I      Numerical Methods for Solving the Time-Dependent
Schrddnger Equation   273
11.1 Spectral Projection and Collocation  275
11.2 The Pseudospectrali Basis 281
11.3 Gaussian Quadrature 285
11-4 Representation of the Hamiltonian in the Reduced Space 293.
11* 5 The Discrete Variable Representation 297
1 .6 The Fourier Method 301
11.7 Time Propagation 31.2
Problems 326
References 329
PART III   Applications     333
CHAPTER 12    Introduction to Molecular Dynamics  335
12.1 The Born-Oppenheirner Approximation 335
12.2 Adiabatic versus Diabatic Representations 338
12.3 Potential Energy Surfaces 345
12,4 Normal Modes of Vibration 352
12.5 Chemical Reactions and Transition State Theory  356
12.6 Symmetry and Permutations 370
12.7 Hyperspherical Coordinates 382
History and Further Reading 387
Problems 388
References 390
CHAPTER 13 Femtosecond Pulse Pair Excitation 395
131 First-Order Processes: Wavepacket Interherometry  395
13.2 Second-Order Processes: Clocking Chemical Reactions 403
13.3 Coherent Nonlinear Spectroscopy 408
14 Density Operator Formulation of Optical Perturbations 419
References 424
CHAPTER 14    One- and Two-Photon Electronic Spectroscopy  427
14.1 Electronic Absorption and Emission Spectroscopy 433
14.2 Transition State Spectroscopy 445
14.3 Resonance Raman Spectroscopy 449
14.4 Dispersed Fluorescence Spectroscopy 465
Problems 473
References 475
CHAPTER 15    Strong Field Excitation  479
15.1 Two-Level System  479
15.2 The Fey"aan-Vern-flellwarr (FVH) Representation 482
15.3 Dressed States 486
15.4 Adiabatic Excitation with Strong Fields 490
15.5 Impulsive Excitation 499
15.6 Optical Paralysis 501
Problems 504
References 505
CHAPTER 16    Design of Femtosecond Pulse Sequences to Control
Chemical Reactions  509
16.1 Intuitive Control Concepts 511.
16.2 Variational Formulation of Control of Product Formation 516
16.3 Applications of the Variational Formulation 528
16A Multiple Pathway Interference 534
16.5 Chirped Pulse Excitation 539
16.6 Learning Algorithms 544
Problems 547
References 553
CHAPTER 17    Wavepacket Approach to Photodissociation   559
17.1 Introduction 559
17.2 The Eigenstates of an Asymptotic Hamiltonian 560
17.3 The Eigenstates of a Scattering Hamiltonian 561
17.4 Mo0ler Operators 566
17.5 Wavepacket Formulation of Photodissociation 569
17.6 Applications 571
References 577
CHAPTER 18 Wavepacket Correlation Function Formulation
of Reactive Scattering  579
18.1 The Concept of an Arrangement Channel and the Problem of
Coordinate Systems 580
18.2 The BEigenstates of a Scattering Hamiltonian with Multiple Arrangement
Channels 581
18.3 Wavepacket Cross-Correlation Function Fomnnulation of S (E) 586
18.4 Application to Coinear H + H  H + H  591
18.5 Cumulative Reaction Probability 594
References 600



Library of Congress subject headings for this publication: Quantum theory