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Graduate Quantum Mechanics

Text Syllabus

Meeting Time

CHM 6938-005 (Quantum Mechanics I) will meet Mondays and Wednesdays from 10:45am-12:00pm in NES 104.

The instructor may be reached anytime by phone 4-4298 or email (username: davidrogers on usf.edu).

Course Overview

Nanoscience has already reached its natural quantum limit, bringing the 'spooky' behavior of quantum systems into the center of a revolution. This course will rigorously develop the fundamentals of quantum mechanics required for understanding the interplay of electricity and magnetism with electronic structure.

Course Objectives

By the end of the course, you will be able to determine which problems in chemistry and physics have an essentially quantum nature. For those that do, you will know the rules for formulating the solution mathematically and the tools and special tricks for completing the solution. You will also learn aspects of numerical solutions and partial differential equations that apply to many aspect of modern technology outside of QM. As a research course, you will be expected to finish with a high-level understanding of where to find worked projects similar to new and open questions, and to mix, match, and evaluate solution techniques before diving into differentiation or trial and error.

Grading

Your work will be graded based on homework assignments (80%) and one student project (20%).

Some Useful Preliminaries

Partial differential equations, linear algebra, Fourier series

These will be reviewed in the course, but undergraduate calculus is required.

Textbooks

• Quantum Mechanics: A Modern and Concise Introductory Course, Daniel Bes (Springer, 2007 (2nd ed) or 2012 (3rd ed))

Bes gives an excellent survey of the myriad applications of QM, and is detailed enough to provide all the tools and intuition needed to do the math. It does as well as anyone should expect in getting at the whys and hows of the confusion that is quantum, including various manifestations of the measurement problem.

eBook

• McQuarrie (Quantum Chemistry, 2nd ed., Univ. Sci. 2007)

McQuarrie focuses in on molecular electronic structure, providing a chemistry compliment to Bes' physics-oriented book. It covers what we need to understand molecular computations, including spectroscopy, thermochemistry, Hartree-Fock and Slater determinants, molecular orbitals, density-functional theory.

Leung and Marshall have written a solutions manual, Problems and Solutions for McQuarrie's QM, Univ. Sci., 2007.

Both these texts are available at the library (possibly in course reserves), and purchasing them is not required for the course.

Other QM Texts

• Pauling (free book on archive.org)
  • Early, but presciently maps out the next ~30 y. of developments
• Atkins
• Griffiths
• Levine
• Shankar (Principles of QM, 2nd ed., Plenum 1994)
  • Introduces Quantization using commutation...
• Landau & Lifschitz 3 & 4
• Advanced Quantum Mechanics, Dick Rainer (Springer, 2012) - chem/phys.
• Bes, QM 2012 edition

Course Outline

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(01) Aug 26

Class intro., failures of classical mechanics, Planck's hypothesis.

(02) Sep 2 (Mon. = Labor Day)

Review of the Schrodinger equation, Heisenberg states and all that. Basic linear algebra.

(03) Sep 9

One-dimensional problems - review of the potential well. New applications for the Helmholtz equation - bound and scattering states.

(04) Sep 16

Applications of the Helmholtz equation, continued - tunneling, radioactive decay and diffraction.

(05) Sep 23

Review of the harmonic oscillator and hydrogen atom, introduction to multi-particle statistics.

(06) Sep 30

Mathematics of rotation and time-dependence. Introduction to spin.

(07) Oct 7

Angular momentum, applied to rotational (radio-wave) spectroscopy electronic and nuclear spin in NMR.

(08) Oct 14

More about those molecular orbitals, and calculations on the H<math>_2</math> atom. If quantum theory is exact, why do I need to choose a bunch of basis functions?

(09) Oct 21

Perturbation theory calculations, also applied to H<math>_2</math>.

(10) Oct 28

Electronic (UV) and vibrational (IR) polarizability.

(11) Nov 4

Thermochemistry and molecular reactions.

(12) Nov 11 (Mon. = Veteran's Day)

Statistics of an electron gas. The Kohn-Sham decomposition and the resulting alphabet soup.

(13) Nov 18

The continuing quest for the perfect functional.

(14) Nov 25 (Fri. Nov 29 = Day after Thanksgiving)

Chemical reactions and transition-state theory.

(15) Dec 2 (Fri. Dec. 6 = Last Class)

Better entanglement for better quantum computers.

(16) Dec 9 - final exam week

List of Group Study Topics

1. Einstein, Podolsky and Rosen's paradox and Bell's inequality.
2. Bohm's quantum interpretation of quantum mechanics (see also Bell's later response)
3. Gaussian-type orbitals, exponents, and integrals for the H<math>_2</math> atom.
4. calculating electron hopping rates using the non-equilibrium Green's function method
5. Eyring's transition-state-theory and reaction diagrams using the empirical valence-bond method.
6. Formulation of QM expectations using path integrals
7. Numerical solution methods for 1D problems.

Choose an interesting topic in groups of no more than 3 students by Friday, Oct. 4.