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Tokmakoff, Andrei, 5.74 Introductory Quantum Mechanics II, Spring 2009. (Massachusetts Institute of Technology: MIT OpenCourseWare),  (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

Introductory Quantum Mechanics II

Spring 2007

Energy diagram for a coupled two-level system (2LS) with a time-independent Hamiltonian. (Image by Andrei Tokmakoff.)

Course Description

This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Technical Requirements

Special software is required to use some of the files in this course: .dat.



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.

  • Time-dependent quantum mechanics (time-evolution operator, two level system, interaction picture, time-dependent perturbation theory)
  • Interaction of light with matter (electric dipole Hamiltonian, absorption and stimulated emission, infrared and electronic absorption lineshape)
  • Correlation function description of spectroscopy (correlation functions, absorption lineshapes)
  • Relaxation (origin of irreversible relaxation)


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 after the last lecture, and should not be discussed with your classmates.

Four problem sets 75%
One take home exam 25%

Academic Honesty

It is expected that students will maintain the highest standards of academic honesty.

With respect to homework assignments, it is expected that no student will turn in work that is not his or her own by copying the work of another student or by using the work or solutions from this course given in previous years. Discussion of approaches to solving the homework problems after attempting to work the problems independently, however, is permitted and encouraged.

It is expected that during a test or examination, a student will not:

  1. Accept or use information of any kind from other students;
  2. Represent the work of another student as his or her own;
  3. Use aids to memory other than those expressly permitted by the examiner.

Following a test or examination, a student will not try to deceive teachers or graders by misrepresenting or altering his or her previous work. In advance of a test or exam, a student will not knowingly obtain access to the exam questions.

Departures from the above standards are contrary to fundamental principles of MIT and of the larger scientific community. Such departures are considered serious offenses for which disciplinary penalties, including suspension and expulsion, can be imposed.


There is no required text for this class. The following books are strongly recommended:

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.

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 Introduction; Time-independent Hamiltonian  
2 Time-development of state amplitudes: Resonant driving of a two-level system  
3 Quantum dynamics: The time-evolution operator Problem set 1 due
4 The Schrodinger, Heisenberg, and interaction pictures  
5 Perturbation theory Problem set 2 due
6 Fermi's golden rule  
7 Irreversible relaxation  
8 Interaction of light and matter Problem set 3 due
9 Electric dipole Hamiltonian and absorption of light  
10 Time-correlation functions  
11 Absorption lineshape from time-correlation functions  
12 Electronic spectroscopy: The displaced harmonic oscillator model Problem set 4 due   Tell A Friend