The field of quantum chemistry seeks to provide a rigorous description of chemical processes at its most fundimental level. For ordinary chemical processes, the most fundimental and underlying theory of chemistry is given by the time-dependent and time-independent version of the Schroedinger equation. However, simply stating an equation that provides the underlying theory in now shape or form yields and predictive or interpretive power. In fact, most of what we do in quautum mechanics is to develop a series of well posed approximation and physical assumptions to solve basic equations of quantum mechanics. In this course, we will delve deeply into the underlying physical and mathematical theory. We will learn how to solve some elementary problems and apply these to not so elementary examples.
As with any course of this nature, the content reflects the instructors personal interests in the field. In this case, the emphasis of the course is towards dynamical processes, transitions between states, and interaction between matter and radiation. More ``traditional" quantum chemistry courses will focus upon electronic structure. In fact, the moniker ``quantum chemistry" typically refers to electronic structure theory. While this is an extremely rich topic, it is my personal opinion that a deeper understanding of dynamical processes provides a broader basis for understanding chemical processes.
The purpose of this course is to provide a solid and mathematically rigorous tour through modern quantum mechanics. We will begin with simple examples which can be worked out exactly on paper and move on to discuss various approximation schemes. For cases in which analytical solutions are either too obfuscating or impossible, computer methods will be introduced using Mathematica. Applications toward chemically relevant topics will be emphasized throughout.
We will primarily focus upon single particle systems, or systems in which the particles are distinguishable. Special considerations for systems of indistinguishable particles, such as the electrons in a molecule, will be discussed towards the end of the course. The pace of the course is fairly rigorous, with emphasis on solving problems either analytically or using computer.
Students are expected to be familiar with the basic results of quantum mechanics at the level presented in junior or senior level physical chemistry. Also, students are expected to be familiar with differential and integral calculus, linear algebra, and elementary differential equations. Students weak in these areas will find this course very difficult.
Homework is due on dates followed by an "H" at the start of class. The homework assignments are posted on the class web pages. No work is accepted after the due date. Topics with a "D" after the date are covered in a discussion format. After the discussion, you can ask questions on any homework problem. Teams will be assigned as discussion leaders for each discussion. Half of your discussion grade is based on how well you lead a discussion and the other half is based on your discussion participation