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Quantum Dynamics

Applications in Biological and Materials Systems

Eric R. Bittner
Publication Date:
July 21, 2009
Content Details:
334 pages

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List Price:   $130.00

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  • About the Book

    Book Summary

    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.


      • 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

    Bohr-Sommerfield Quantization

    The WKB Approximation

    Connection Formulas


    Problems and Exercises

    Quantum Dynamics (and Other Un-American Activities)


    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



    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


    Problems and Exercises

    Lattice Models for Transport and Structure


    Stationary States on a Lattice

    Kronig-Penney Model

    Quantum Scattering and Transport

    Defects on Lattices

    Multiple Defects