Courant Institute of Mathematical Sciences
Department of Mathematics
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.
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.