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
The Free Particle Wave Packet
1. General Solution
2. The Center of the Wavepacket
3. The Dispersion of the Wavepacket
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
Classical-Quantum Correspondence
1. Ehrenfest's Theorem
2. Bohmian Mechanics and the Classical Limit
3. Fractional Revivals
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
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
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

Formal Theory and Methods of Approximation

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
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
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
Numerical Methods
1. Spectral and Pseudospectral Representation
2. Pscudospectral Calculation of Matrix Elements
3. Discrete Variable Represenation
4. The Fourier Method
5. Time Propagation

Applications

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
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
One- and Two-Photon Electronic Spectroscopy
1. Electronic Absorption and Emission Spectroscopy
2. Transition State Spectroscopy
3. Resonance Raman Spectroscopy
4. Dispersed Fluorescence Spectroscopy
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
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
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
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
4. Application to Collinear
5. Cumulative Reaction Probability

Table of Contents

Pictures and Concepts

Formal Theory and Methods of Approximation

Applications