Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Overview
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
Grading
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.
| ACTIVITIES | PERCENTAGES |
|---|---|
| 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.
Textbooks
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.
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.
Calendar
| LEC # | TOPICS | KEY DATES |
|---|---|---|
| Quantum mechanics | ||
| 1 | Time-independent Hamiltonian | |
| 2 | Time-dependent Hamiltonian | |
| 3 | Irreversible relaxation | |
| 4 |
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 |
