Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session

Prerequisites

The prerequisites for this course are:

8.03 Physics III: Vibrations and Waves, 18.03 Differential Equations, and 5.61 Physical Chemistry.

Professor Field’s Fall 2017 version of this 5.61 Physical Chemistry includes a full set of video lectures and lecture notes.

Course Description

This is a course for users, rather than admirers, of quantum mechanics. It will wind its way, with a minimum of elegance and philosophical correctness, through a progression of increasingly complex (mostly) time-independent problems.

We will begin with one-dimensional problems, treated in the Schrödinger Ψ(x) wavefunction picture. Then Dirac's bra-ket notation will be introduced and we will switch permanently to Heisenberg's matrix mechanics picture. In matrix mechanics all information resides in a collection of numbers called “matrix elements” and all sorts of trickery will be developed to find ways of deriving the values of all matrix elements without ever actually evaluating any integrals! One should never underestimate the importance of perturbation theory. Armed with matrices, we will turn to 3-D central force (spherical symmetry) problems, and discover that for all spherical systems (atoms), the angular factors of all matrix elements are trivially evaluable without approximation. Key topics are commutation rule definitions of scalar, vector, and spherical tensor operators, the Wigner-Eckart theorem, and 3j (Clebsch-Gordan) coefficients. Finally, we deal with many-body systems, exemplified by many-electron atoms (“electronic structure”), anharmonically coupled harmonic oscillators (“intramolecular vibrational redistribution: IVR”), and periodic solids.

Textbooks

Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics. Vol. 1. Wiley-VCH, 1st edition, 1992. ISBN: 9780471569527.

Cohen-Tannoudji, C., B. Diu, and F. Laloë. Quantum Mechanics. Vol. 2. Wiley-VCH, 1st edition, 1991. ISBN: 9780471164357.

The point of view of the text is quite different from the lectures (the text is more elegant, analytical, and logical). Reading assignments are intended to complement the lectures. Most homework, but few exam problems, will be based on the text. Additional reading material will be handed out in class.

Other Books

Field, Robert W. Spectra and Dynamics of Small Molecules: Alexander Von Humboldt Lectures. Springer, 2015. ISBN: 9783319159577.

Tinkham, Michael. Group Theory and Quantum Mechanics. Dover Publications, 2003. ISBN: 9780486432472.

Golding, R.M. Applied Wave Mechanics. Van Nostrand, 1969. ISBN: 9780442027469.

Condon, Edward Uhler, and George Shortley. The Theory of Atomic Spectra. Cambridge University Press, 1935.  ISBN: 9780521092098.

Karplus, Martin, and Richard N. Porter. Atoms and Molecules. Addison-Wesley, 1970. ISBN: 9780805352184.

Baym, Gordon. Lectures on Quantum Mechanics. Benjamin Cummings Publishing Company, 1969. ISBN: 9780805306675.

Assignments

Problem Sets

There will be ten weekly problem sets, which should be handed in at the start of class on the specified due date and will be graded.

Exams

There will be two take-home, open-book exams. A key difference between problems and the exams is that out-of-class discussion of the problems, but not of the exams, is expected. 

Grading