Quantum Dynamics
Applications in Biological and Materials Systems
 Edition:
 1st
 Author(s):
 Eric R. Bittner
 ISBN:
 9781420080537
 Format:
 Hardback
 Publication Date:
 July 21, 2009
 Content Details:
 334 pages
 Language:
 English
Also of Interest

About the Book
Book Summary
Even though timedependent 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 onesemester quantum chemistry course and the modern field of chemical dynamics, presenting the quantum theory of charge and energy transport in biological systems and opticalelectronic materials from a dynamic perspective.
Reviews the basics
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.
Timeindependent and timedependent perspectives
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 twolevel system. This is discussed with a timeindependent as well as a timedependent perspective. The book also explores what happens when the twolevel 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 pi electronic structure of conjugated organic systems and discuss electronphonon coupling in conjugated systems and transport and dynamics in extended systems.
Includes Mathematica^{®} downloads
On an accompanying website, 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 website combine to provide students with a clear understanding of the theory and its applications.
Features
 Covers cutting edge material rarely found in textbooks
 Provides required background and theoretical material to understand the concepts
 Discusses applications of current interest, as well as many theoretical topics not presented well in other books
 Offers Mathematica^{® }applications and codes on an accompanying website to illustrate the theoretical methods presented

Contents
Survey of Classical Mechanics
Newton’s Equations of Motion
Lagrangian Mechanics
Conservation Laws
Hamiltonian Dynamics
Problems and Exercises
Waves and Wave Functions
Position and Momentum Representation of Psi
The Schrödinger Equation
Particle in a Box
Problems and Exercises
Semiclassical Quantum Mechanics
BohrSommerfield Quantization
The WKB Approximation
Connection Formulas
Scattering
Problems and Exercises
Quantum Dynamics (and Other UnAmerican Activities)
Introduction
The Twostate System
Perturbative Solutions
Dyson Expansion of the Schrödinger Equation
Timedependent Schrödinger Equation
Time Evolution of a Twolevel System
Timedependent Perturbations
Interaction between Matter and Radiation
Application of Golden Rule: Photoionization of Hydrogen 1s
Coupled Electronic/Nuclear Dynamics
Problems and Exercises
Representations and Dynamics
Schrödinger Picture: Evolution of the State Function
Heisenberg Picture: Evolution of Observables
Quantum Principle of Stationary Action
Interaction Picture
Problems and Exercises
Quantum Density Matrix
Introduction: Mixed vs Pure States
Time Evolution of the Density Matrix
Reduced Density Matrix
The Density Matrix for a Twostate System
Decoherence
Summary
Problems and Exercises
Appendix: Wigner Quasiprobability Distribution
Excitation Energy Transfer
DipoleDipole Interactions
Förster’s Theory
Beyond Förster
Transition Density Cube Approach
Electronic Structure of Conjugated Systems
Pi Conjugation in Organic Systems
Hückel Model
Electronic Structure Models
Neglect of Differential Overlap
An Exact Solution: INDO Treatment of Ethylene
Ab Initio Treatments
Creation/Annhiliation Operator Formalism for Fermion Systems
Problems and Exercises
ElectronPhonon Coupling in Conjugated Systems
SuSchriefferHeeger Model for Polyacetylene
Exciton Selftrapping
Davydov’s Soliton
Vibronic Relaxation in Conjugated Polymers
Summary
Problems and Exercises
Lattice Models for Transport and Structure
Representations
Stationary States on a Lattice
KronigPenney Model
Quantum Scattering and Transport
Defects on Lattices
Multiple Defects
Appendix
References
Index