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Quantum Dynamics

Applications in Biological and Materials Systems

By Eric R. Bittner

Published July 21st 2009 by CRC Press – 334 pages

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Description

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.

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.

Time-independent and time-dependent 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 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 pi electronic structure of conjugated organic systems and discuss electron-phonon 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.

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

Bohr-Sommerfield Quantization

The WKB Approximation

Connection Formulas

Scattering

Problems and Exercises

Quantum Dynamics (and Other Un-American Activities)

Introduction

The Two-state System

Perturbative Solutions

Dyson Expansion of the Schrödinger Equation

Time-dependent Schrödinger Equation

Time Evolution of a Two-level System

Time-dependent 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 Two-state System

Decoherence

Summary

Problems and Exercises

Appendix: Wigner Quasi-probability Distribution

Excitation Energy Transfer

Dipole-Dipole 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

Electron-Phonon Coupling in Conjugated Systems

Su-Schrieffer-Heeger Model for Polyacetylene

Exciton Self-trapping

Davydov’s Soliton

Vibronic Relaxation in Conjugated Polymers

Summary

Problems and Exercises

Lattice Models for Transport and Structure

Representations

Stationary States on a Lattice

Kronig-Penney Model

Quantum Scattering and Transport

Defects on Lattices

Multiple Defects

Appendix

References

Index

Author Bio

Eric Bittner is currently John and Rebecca Moores Distinguished Professor of chemical physics at the University of Houston. He received his PhD from the University of Chicago in 1994 and was a National Science Foundation Postdoctoral Fellow at the University of Texas at Austin and Stanford University before moving to the University of Houston in 1997. His accolades include an NSF Career Award and a Guggenheim Fellowship. He has also held visiting appointments at the University of Cambridge, the École Normale Supérieure–Paris, and at Los Alamos National Lab. His research is in the area of quantum dynamics as applied to organic polymer semiconductors, object linking and embedding directory services (OLEDS), solar cells, and energy transport in biological systems.