Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


This class will be covered in twelve, 1.5 hour lectures. We will cover topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. There will also be an extra 4 lectures focusing on nonlinear spectroscopy.

  • Time-dependent quantum mechanics
  • Interaction of light with matter
  • Correlation function description of condensed phase spectroscopy
  • Fluctuations and relaxation
  • Nonlinear spectroscopy


There will be 4 problem sets worth a total of 75% of the grade, which can and should be worked on together. A take-home exam will account for the remaining 25% of the grade. It will be distributed during the last lecture, and should not be discussed with your classmates.

Four problem sets 75%
One take-home exam 25%


Mathematical Software

The problem sets in this class will include numerical problems that require you to solve one-dimensional Schrödinger equations, integrate coupled differential equations, and other problems involving the manipulation of matrices and vectors. For this, the most convenient approach is using some type of mathematical or engineering calculation software. If you have little experience with this, I recommend Mathcad(R) 14, because I will distribute Mathcad worksheets with sample routines on this Web site.


Buy at Amazon Nitzan, Abraham. Chemical Dynamics in Condensed Phases. New York, NY: Oxford University Press, 2006. ISBN: 9780198529798.
This is a wonderful new book that thoroughly covers all topics that you might care to learn about for time-dependent quantum mechanics relevant to the condensed phase. We will follow the treatment of several topics in this book.

Buy at Amazon Schatz, George C., and Mark A. Ratner. Quantum Mechanics in Chemistry. Mineola, NY: Dover Publications, 2002. ISBN: 9780486420035.
This is an important book to have. It has the most overlap with the topics we will cover, uses a similar language and notation, and treats the problems at a similar level.


Quantum mechanics
1 Time-independent Hamiltonian  
2 Time-dependent Hamiltonian  
3 Irreversible relaxation  

Classical description of spectroscopy

Interaction of light and matter

Absorption cross-section

5 Time correlation functions Assignment 1 due
6 Absorption lineshapes  
7 Linear response theory  
8 Displaced harmonic oscillator Assignment 2 due
9 Fluctuations: Gaussian stochastic model Assignment 3 due
10 Fluctuations: energy gap Hamiltonian  
11 Vibrational relaxation  
12 Density matrix Assignment 4 due
Nonlinear spectroscopy boot camp
13 Nonlinear polarization Assignment 5 due
14 Diagrammatic perturbation theory  
15 Third order spectroscopy  
16 Characterizing fluctuations  
17 Two-dimensional spectroscopy

Nonlinear spectroscopy
problems due