All About Chemistry... 2011 and beyond

Introductory Quantum Mechanics II

Course Home
Study Materials
Course Resources
  • 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."

    Note: Contents for this page are Licensed from under the Creative Commons Attribution Share-Alike license.

    Massachusetts Institute of Technology

    Course Code

    Date Taught
    Spring/Summer 2009

    Graduate (First Year)
  • 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.


    Amazon logo 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.

    Amazon logo 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.


    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

  • Lectures
    Introductory Quantum Mechanics II - Lecture 13 - Prof. Andrei Tokmakoff View
    Introductory Quantum Mechanics II - Lecture 14 - Prof. Andrei TokmakoffView
    Introductory Quantum Mechanics II - Lecture 15 - Prof. Andrei TokmakoffView
    Introductory Quantum Mechanics II - Lecture 16 - Prof. Andrei TokmakoffView
  • DescriptionTypeLink
    Problem set 0DownloadClick
    Problem set 1DownloadClick
    Problem set 2DownloadClick
    Trajectory for problem 3DownloadClick
    Problem set 3DownloadClick
    Problem 4DownloadClick
    Problem set 5DownloadClick
    Nonlinear spectroscopy problemsDownloadClick
  • DescriptionTypeLink
    Two-Level systemDownloadClick
    Resonant driving of 2LSDownloadClick
    Displaced harmonic oscillator lineshape: couplingDownloadClick
    Displaced harmonic oscillator lineshape: temperatureDownloadClick
    Gaussian stochastic model for lineshapeDownloadClick
  • DescriptionTypeLink
    Course Materials DownloadDownloadClick
    Lecture Note 13 - Nonlinear polarizationDownloadClick
    Lecture Note 14 - Diagrammatic perturbation theory DownloadClick
    Lecture Note 15 - Third order spectroscopy DownloadClick
    Lecture Note 16 - Characterizing Fluctuations DownloadClick
    Lecture Noe 17 - Two-dimensional spectroscopyDownloadClick
Social Networking

Please recommend us on Facebook, Twitter and more:

Other social media tools

Global Partners

Tell us what you think of Chemistry 2011 -- we welcome both positive and negative comments. Have any problems using the site? Questions?

About us

Chemistry2011 is an informational resource for students, educators and the self-taught in the field of chemistry. We offer resources such as course materials, chemistry department listings, activities, events, projects and more along with current news releases.

Events & Activities

Are you interested in listing an event or sharing an activity or idea? Perhaps you are coordinating an event and are in need of additional resources? Within our site you will find a variety of activities and projects your peers have previously submitted or which have been freely shared through creative commons licenses. Here are some highlights: Featured Idea 1, Featured Idea 2.

About you

Ready to get involved? The first step is to sign up by following the link: Join Here. Also don’t forget to fill out your profile including any professional designations.

Global Partners