Table of Contents

    Pictures and Concepts

  1. The Time Dependent Schrödinger Equation
    1. Separation of Variables and Reconstitution of the Wavepacket
    2. Expectation Values
    3. A Worked Example: Particle in Half a Box
  2. The Free Particle Wave Packet
    1. General Solution
    2. The Center of the Wavepacket
    3. The Dispersion of the Wavepacket
  3. The Gaussian Wavepacket
    1. The Gaussian Free Particle
    2. General Properties of Gaussian Wavepackets
    3. Gaussian in a Quadratic Potential
    4. Reexamination of the Stationary Phase Method
  4. Classical-Quantum Correspondence
    1. Ehrenfest's Theorem
    2. Bohmian Mechanics and the Classical Limit
    3. Fractional Revivals
  5. The Wigner Representation
    1. The Concept of Phase Space
    2. The Wigner Representation of Wavepackets
    3. The Density Operator
    4. Wigner Representation of the Density Operator
  6. Correlation Functions and Spectra
    1. Spectra as Fourier Transforms of Wavcpackct Correlation Functions
    2. General Properties of Fourier Transforms
    3. Eigenfunctions as Fourier Transforms of Wavepackets
  7. One Dimensional Barrier Scattering
    1. Wavepacket Formulation of Reflection and Transmission Coefficients
    2. Cross-Correlation Function Formulation
    3. Scattering Eigenstates
    4. Reconstituting the Wavepacket from the Scattering Eigenstates
    5. Resonances and Time Delay

    8. Formal Theory and Methods of Approximation

  8. Linear Algebra and Quantum Mechanics
    1. Linear Vector Spaces
    2. Operators: Mapping a Wavefunction to Another Wavefunction
    3. Discrete Basis Sets
    4. Continuous Basis Sets
  9. Approximate Solutions
    1. The Schrödingcr, Heisenberg and Interaction Pictures
    2. Time Dependent Perturbation Theory
    3. The Magnus Expansion
    4. Adiabatic Dynamics and the Geometrical Phase
    5. Periodic Hamiltonians and Floquet Theory
    6. Variational Principles and the Time-Dependent Hartree Approximation
  10. Semiclassical Mechanics
    1. The Classical Action
    2. Path Integration
    3. The van Vleck Propagator
    4. The Propagator as a Unitary Transformation
    5. Gaussian Wavepackcts and the van Vleck Propagator
  11. Numerical Methods
    1. Spectral and Pseudospectral Representation
    2. Pscudospectral Calculation of Matrix Elements
    3. Discrete Variable Represenation
    4. The Fourier Method
    5. Time Propagation

    12. Applications

  12. Introduction to Molecular Dynamics
    1. The Born-Oppenheimer Approximation
    2. Adiabatic vs. Diabatic Representations
    3. Potential Energy Surfaces
    4. Normal Modes of Vibration
    5. Chemical Reactions and Transition State Theory
    6. Symmetry and Permutations
    7. Hyperspherical Coordinates
  13. Femtosecond Pulse Pair Excitation
    1. First Order Processes: Wavepacket Interferometry
    2. Second Order Processes: Clocking Chemical Reactions
    3. Coherent Nonlinear Spectroscopy
    4. Density Operator Formulation of Optical Perturbations
  14. One- and Two-Photon Electronic Spectroscopy
    1. Electronic Absorption and Emission Spectroscopy
    2. Transition State Spectroscopy
    3. Resonance Raman Spectroscopy
    4. Dispersed Fluorescence Spectroscopy
  15. Strong Field Excitation
    1. Two-level system
    2. The Feynman-Vernon-Hellwarth (FVH) Representation
    3. Adiabatic Excitation: Population transfer in a 3-Level System
    4. Impulsive Excitation
    5. Heating and Cooling of Molecular Internal Degrees of Freedom
  16. Design of Femtosecond Poise Sequences to Control Reactions
    1. Pump-Dump Scheme
    2. Variational Formulation of Control of Product Formation
    3. Applications of the Variational Formulation
    4. Multiple Pathway Interference
    5. Chirped Pulse Excitation
    6. Learning Algorithms
  17. Wavepacket Approach to Photodissociation
    1. Introduction
    2. The Eigenstates of an Asymptotic Hamiltonian
    3. The Eigenstates of a Scattering Hamiltonian
    4. Møller Operators
    5. Wavcpackct Formulation of Photodissociation
    6. Applications
  18. Wavepacket Approach to Reactive Scattering
    1. The Concept of an Arrangement Channel
    2. Scattering Eigenstates for Multiple Arrangements
    3. Wavcpackct Cross-Correlation Function Formulation of The Actual Formula
    4. Application to Collinear The Actual Formula
    5. Cumulative Reaction Probability