# Quantum Mechanics and Electronic Structure

Fall 2001

Courant Institute of Mathematical
Sciences

Department of Mathematics

Jonathan Goodman

## Overview

This is an applied mathematician's introduction to quantum mechanics with
application to electronic structure and properties of materials. We will
discuss the basic physical problems such as the electronic structure of
atoms and simple molecules, the band structure and fermi liquid theories
of electrons in crystals, and perturbations of these. We will cover
variational and heuristic approximation techniques such as Hartree-Fock and
Kohn-Sham together with more rigorous but limited computational techniques
including quantum monte carlo. There are many open problems in this area.

## Course materials to download

Lecture 1, Introduction to the Schroedinger equation, in
postscript format, or
pdf format for the acrobat reader. Note that
this set of notes ends with some problems that registered students are
expected to hand in by October 2. These notes were written in a hurry
and contain errors ranging from simple misspellings to major misunderstandings.
I would be grateful for people attending the lectures to provide feedback
on the notes.

Lecture 2, The harmonic oscillator, in
postscript format, or
pdf format for the acrobat reader.

Lecture 3, The hydrogen atom, I: radial states, in
postscript format, or
pdf format for the acrobat reader.

The final exam, in postscript format or in
pdf format. It is due at the end of finals week.