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Description

This is a graduate-level course in advanced quantum mechanics as it applies to chemistry. We will begin by reviewing such mathematical prerequisites as complex vector spaces, eigenvectors and eigenvalues, operators, inner and outer products, dual spaces, and commutators. We will review some advanced concepts in angular momentum (ladder operators, addition of angular momenta, etc). We will discuss in detail variational and perturbation methods. Advanced topics such as spin, degenerate and time-dependent perturbation theory, and interaction of light with matter will also be discussed. The remainder of the course discusses electronic structure theory, starting from a detailed look at the Born-Oppenheimer approximation, followed by a general discussion of electronic structure and an introduction to the Hartree-Fock approximation (i.e., molecular orbital theory), and concluding with a survey of theoretical models in quantum chemistry. A few applications to spectroscopy are discussed or covered in problem sets throughout the course.

Syllabus

Course Syllabus

Required Textbooks

1. R. Shankar, Principles of Quantum Mechanics, 2nd ed. (Plenum, New York, 1994). Intermediate-level physics book.
2. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Introduction to Advanced Electronic Structure Theory, 1st ed., revised (Dover, 1989). Covers the electronic structure part.

Recommended Supplementary Books

1. I. N. Levine, Quantum Chemistry, 4th ed. (Prentice Hall, Englewood Cliffs, NJ, 1991). Covers many of the topics in this course at a slightly lower level.
2. G. Strang, Linear Algebra and its Applications, 3rd Ed., (Harcourt Brace Jovanovich, San Diego, 1988). Good intro to linear algebra.
3. D. A. McQuarrie, Quantum Chemistry (University Science Books, Mill Valley, CA, 1983). Very readable introductory text.
4. E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley, New York, 1998). Advanced physics text.

Notes

• List of Concepts
• Quantum Chemistry Lecture Notes
• Notes on Elementary Linear Algebra (PDF)
• A Brief Review of Elementary Quantum Chemistry (PDF)
• Time Evolution in Quantum Mechanics (PDF)
• IR Spectroscopy: Parts 1 and 2
• Summary of Angular Momentum (PDF)
• The Born-Oppenheimer Approximation (PDF)
• Basis Sets
• Intro to Electron Correlation

Problem sets:

Problem Set 1

Announcements

Do not forget to study the book carefully. Much of the course basically follows the book, so it should be obvious what portions you need to read.