Quantum dynamics: applications in biological and materials systems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2010
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XI, 322 S. graph. Darst. |
| ISBN: | 9781420080537 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
...................................................................ix
About the Author
.........................................................xi
Chapter
1
Survey of Classical Mechanics
...................................1
1.1
Newton s Equations of Motion
.............................2
1.1.1
Newton s Postulates
...............................2
1.2
Lagrangian Mechanics
....................................5
1.2.1
The Principle of Least Action
......................5
1.2.2
Example: Three-Dimensional Harmonic Oscillator
in Spherical Coordinates
...........................7
1.3
Conservation Laws
.......................................10
1.3.1
Conservative Forces
..............................11
1.4
Hamiltonian Dynamics
...................................13
.4.1
Phase Plane Analysis
.............................17
.4.2
Interaction between a Charged Particle and an
Electromagnetic Field
............................18
.4.3
Time Dependence of a Dynamical Variable
.........19
.4.4
Virial Theorem
..................................20
.4.5
Angular Momentum
.............................21
.4.6
Classical Motion of an Electron about a Positive
Charge (Nucleus)
................................22
.4.7
Birth of Quantum Theory
.........................22
.4.8
Do the Electron s
Orbitals
Need to Be Circular?
___25
.4.9
Wave-Particle Duality
............................27
.4.10 De
Brogue s Matter Waves
.......................29
1.5
Problems and Exercises
..................................30
Chapter
2
Waves and Wave Functions
....................................33
2.1
Position and Momentum Representation of
ψ)
.............34
2.2
The
Schrödinger
Equation
................................35
2.2.1
Gaussian Wave Functions
.........................36
2.2.2
Evolution of
ψ {χ)...............................
38
2.3
Particle in a Box
.........................................40
2.3.1
Infinite Box
.....................................40
2.3.2
Particle in a Finite Box
...........................42
2.3.3
Scattering States and Resonances
..................44
2.3.4
Application: Quantum Dots
.......................47
2.4
Problems and Exercises
..................................52
Chapter
3
Semiclassical Quantum Mechanics
..............................57
3.1
Bohr-Sommerfield Quantization
..........................58
3.2
The Wentzel, Kramers, and Brillouin Approximation
........60
VI
Contents
3.2.1
Asymptotic Expansion for Eigenvalue Spectrum
----60
3.2.2
Example: Semiclassical Estimate of Spectrum
for Harmonic Oscillator
..........................63
3.2.3
The Wentzel
,
Kramers, and Brillouin
Wave Function
..................................63
3.2.4
Semiclassical Tunneling and Barrier Penetration
----65
3.3
Connection Formulas
....................................68
3.4
Scattering
...............................................73
3.4.1
Classical Scattering
..............................73
3.4.2
Scattering at Small Deflection Angles
..............76
3.4.3
Quantum Treatment
..............................77
3.4.4
Semiclassical Evaluation of Phase Shifts
...........79
35
Problems and Exercises
..................................82
Chapter
4
Quantum Dynamics (and Other Un-American Activities)
..........85
4.1
Introduction
.............................................85
4.2
The Two-State System
...................................86
4.3
Perturbative Solutions
....................................88
4.3.1
Dipole
Molecule in Homogenous Electric Field
.....90
4.3.1.1
Weak Field Limit
...................... . .91
4.3.1.2
Strong Field Limit.
......................93
4.4
Dyson Expansion of the Schrodinger Equation
..............93
4.4.1
van
der Waals
Forces: Origin of Long-Range
Attractions
......................................96
4.4.2
Attraction between an Atom and a Conducting
Surface
.........................................98
4Ü
Time-Dependent Schrodinger Equation
....................99
4.6
Time Evolution of a Two-Level System
...................101
4.7
Time-Dependent Perturbations
...........................102
4.7.1
Harmonic Perturbation
..........................104
4.7.2
Correlation Functions
...........................106
4.8
Interaction between Matter and Radiation
.................
Ill
4.8.1
Fields and Potentials of a Light Wave
.............
Ill
4.8.2
Interactions at Low Light Intensity
...............113
4.8.2.1
Oscillator Strength
.....................117
4.8.3
Spontaneous Emission of Light
..................117
4.9
Application of Golden Rule: Photoionization
of Hydrogen Is
.........................................122
4.10
Coupled Electronic/Nuclear Dynamics
....................124
4.10.1
Electronic Transition Rates
.....................128
4.10.2
Marcus Treatment of Electron Transfer
.........131
4.10.3
Including Vibrational Dynamics
.................133
4Л1
Problems and Exercises
.................................138
Chapter
5
Representations and Dynamics
................................145
5.1
Schrodinger Picture: Evolution of the State Function
.......145
5.1.1
Properties of the Time-Evolution Operator
........146
Contents
5.2 Heisenberg
Picture:
Evolution
of
Observables
.............147
5.3 Quantum
Principle of Stationary Action
...................152
5.4
Interaction Picture
......................................156
5.5
Problems and Exercises
.................................159
Suggested Reading
...........................................160
Chapter
6
Quantum Density Matrix
.....................................161
6.1
Introduction: Mixed vs. Pure States
.......................161
6.2
Time Evolution of the Density Matrix
.....................163
6.3
Reduced Density Matrix
.................................164
6.3.1 von
Neumann Entropy
..........................166
6.4
The Density Matrix for a Two-State System
...............166
6.4.1
Two-Level System under Resonance
Coupling—Revisited
............................167
6.4.2
Photon Echo Experiment
........................173
6.4.3
Relaxation Processes
............................174
6.5
Decoherence
...........................................178
6.5.1
Decoherence by Scattering
......................179
6.5.2
The Quantum
Zeno
Effect
.......................184
6.6
Summary
..............................................186
6.7
Appendix: Wigner Quasi-Probability Distribution
..........187
6.7.1
Wigner Representation on a Lattice:
Exciton Diffusion
...............................192
6.7.2
Enforcing Fermi-Dirac Statistics
.................194
6.7.3
The k,
Δ
Representation
........................196
6.8
Problems and Exercises
.................................199
Chapter
7
Excitation Energy Transfer
....................................203
7.1 Dipole-Dipole
Interactions
..............................204
7.2 Förster s
Theory
........................................206
7.3
Beyond
Förster.........................................210
7.4
Transition Density Cube Approach
.......................213
Suggested Reading
...........................................217
Chapter
8
Electronic Structure of Conjugated Systems
....................219
8.1
π
Conjugation in Organic Systems
.......................219
8.2
Hiickel Model
..........................................222
8.2.1
Justification for the Hiickel Model
................224
8.2.2
Example:
13
Butadiene
.........................226
8.2.3
Cyclic Systems
.................................228
8.2.4
Summary of Results from the Hiickel Model
......230
82.5
Alternant Systems
..............................231
8 2.6
Why Bother with the Hiickel Theory?
.............235
8.3
Electronic Structure Models
.............................235
8.3.1
Hartree-Fock Approximation
....................236
83.2
Variational Derivation of the Hartree-Fock
Approach
......................................239
VIII
Contents
8.4
Neglect of Differential Overlap
..........................240
8.5
An Exact Solution:
INDO
Treatment of
Ethylene
..........242
8.5.1
HFTreatment of
Ethylene
.......................245
8.6
Ab Initio
Treatments
....................................248
8.7
Creation/Annhiliation Operator Formalism
for Fermion Systems
....................................249
8.7.1
Evaluating Fermion Operators
...................256
8.7.2
Notation for Two-Body Integrals
.................257
8.8
Problems and Exercises
.................................258
Suggested Reading
...........................................258
Chapter
9
Electron-Phonon Coupling in Conjugated Systems
..............261
9.1
Su-Schrieffer-Heeger Model for Polyacetylene
............261
9.2
Exciton Self-Trapping
...................................264
9.3
Davydov s Soliton
......................................268
9.3.1
Approximate Gaussian Solution
..................272
9.3.2
Exact Solution
.................................273
9.3.3
Discussion: Do
Solitons
Exist in Real
α
-Helix Systems?
...............................274
9.4
Vibronic Relaxation in Conjugated Polymers
..............275
9.5
Summary
..............................................281
9.6
Problems and Exercises
.................................281
Chapter
10
Lattice Models for Transport and Structure
....................283
10.1
Representations
......................................283
10.1.1
Bloch Functions
.............................283
10.1.2
Wannier Functions
...........................285
10.2
Stationary States on a Lattice
..........................286
10.2.1
A Simple Band-Structure Calculation
..........290
10.3
Kronig-Penney Model
................................291
10.4
Quantum Scattering and Transport
.....................293
10.5
Defects on Lattices
...................................295
10.6
Multiple Defects
.....................................298
Appendix Miscellaneous Results and Constants
...........................301
References
..............................................................315
Index
...................................................................321
UAMTUM DYNAMICS
Even though time-dependent spectroscopic techniques continue to push the frontier
of chemical physics, they receive scant mention in introductory courses and are
poorly covered in standard texts. Quantum Dynamics: Applications in Biological
and Materials Systems bridges the gap between what is traditionally taught in
a one-semester quantum chemistry course and the modern field of chemical
dynamics, presenting the quantum theory of charge and energy transport in
biological systems and optical-electronic materials from a dynamic perspective.
Taking a pedagogical approach, the book begins by reviewing the concepts of
classical mechanics that are necessary for studying quantum mechanics. It
discusses waves and wave functions and then moves on to an exploration of
semiclassical quantum mechanics methods, an important part of the development
and utilization of quantum theory.
The main focus of the book is the chapter on quantum dynamics, which begins
with a brief review of the bound states of a coupled two-level system. This is
discussed with a time-independent as well as a time-dependent perspective. The
book also explores what happens when the two-level system has an additional
harmonic degree of freedom that couples the transitions between the two states.
The book reviews different ways in which one can represent the evolution of a
quantum state, explores the quantum density matrix, and examines the basis for
excitation energy transfer between molecules. Later chapters describe the
π
electronic structure of conjugated organic systems and discuss electron-phonon
coupling in conjugated systems and transport and dynamics in extended systems.
On an accompanying Web site.
Mathematica®
applications and codes can be
downloaded to illustrate the theoretical methods presented, and the book offers
ample references for further study. The book and Web site combine to provide
students with a clear understanding of the theory ami its applications.
|
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| indexdate | 2024-07-09T21:53:08Z |
| institution | BVB |
| isbn | 9781420080537 |
| language | English |
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| physical | XI, 322 S. graph. Darst. |
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| publishDateSort | 2010 |
| publisher | CRC Press |
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| spelling | Bittner, Eric R. Verfasser (DE-588)13913946X aut Quantum dynamics applications in biological and materials systems Eric R. Bittner Boca Raton [u.a.] CRC Press 2010 XI, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Quantum theory Textbooks Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Quantenchemie (DE-588)4047979-1 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018005631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018005631&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bittner, Eric R. Quantum dynamics applications in biological and materials systems Quantentheorie Quantum theory Textbooks Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047979-1 (DE-588)4047989-4 |
| title | Quantum dynamics applications in biological and materials systems |
| title_auth | Quantum dynamics applications in biological and materials systems |
| title_exact_search | Quantum dynamics applications in biological and materials systems |
| title_full | Quantum dynamics applications in biological and materials systems Eric R. Bittner |
| title_fullStr | Quantum dynamics applications in biological and materials systems Eric R. Bittner |
| title_full_unstemmed | Quantum dynamics applications in biological and materials systems Eric R. Bittner |
| title_short | Quantum dynamics |
| title_sort | quantum dynamics applications in biological and materials systems |
| title_sub | applications in biological and materials systems |
| topic | Quantentheorie Quantum theory Textbooks Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Textbooks Quantenchemie Quantenmechanik |
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