Mathematical Problems in Solid State Physics

This talk is an introduction to the mathematics of solid state physics. I assume no prior knowledge of the subject beyond that of a graduate student in mathematics or theoretical physics.

The main focus of the talk is quantum mechanics of independent electrons in electric and magnetic fields. After exploring the multitude of possible types of spectra by virtue of examples, we familiarize ourselves with the most basic tool in solid state physics/periodic differential equations: Bloch/Floquet theory. We examine the scope and results of this theory, and we also notice its limitations. Finally we hint at possible extentions.