ACTIVITIES | PERCENTAGES |
---|---|

Four problem sets | 75% |

One take-home exam | 25% |

### Course Description

This course covers 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.

### About Prof. Andrei Tokmakoff

Prof. Andrei Tokmakoff has pioneered novel methods of ultrafast vibrational spectroscopy. He was first to utilize high order grating techniques for the investigation of the molecular dynamics of chemical and biological processes in solution. This was developed into two-dimensional infrared spectroscopy, which allows to capture information on transient molecular structure and characterize structural variation. For the experiments he has progressed the generation of tunable infrared femtosecond pulses and continues to do so. His experiments are complemented by theoretical work on nonlinear spectroscopy, statistical mechanical modeling of dynamics and relaxation, and molecular dynamics computer simulations."

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## 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

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

problems dueLectures Introductory Quantum Mechanics II - Lecture 13 - Prof. Andrei Tokmakoff View Introductory Quantum Mechanics II - Lecture 14 - Prof. Andrei Tokmakoff View Introductory Quantum Mechanics II - Lecture 15 - Prof. Andrei Tokmakoff View Introductory Quantum Mechanics II - Lecture 16 - Prof. Andrei Tokmakoff View Description Type Link Problem set 0 Download Click Problem set 1 Download Click Problem set 2 Download Click Trajectory for problem 3 Download Click Problem set 3 Download Click Problem 4 Download Click Problem set 5 Download Click Nonlinear spectroscopy problems Download Click Description Type Link Two-Level system Download Click Resonant driving of 2LS Download Click Displaced harmonic oscillator lineshape: coupling Download Click Displaced harmonic oscillator lineshape: temperature Download Click Gaussian stochastic model for lineshape Download Click Description Type Link Course Materials Download Download Click Lecture Note 13 - Nonlinear polarization Download Click Lecture Note 14 - Diagrammatic perturbation theory Download Click Lecture Note 15 - Third order spectroscopy Download Click Lecture Note 16 - Characterizing Fluctuations Download Click Lecture Noe 17 - Two-dimensional spectroscopy Download Click