Periodic Homogenization and Effective Mass Theorems for the Schrödinger Equation

Abstract

The goal of this course is to give an introduction to periodic homogenization theory with an emphasis on applications to Schrodinger equation. We review the formal method of two-scale asymptotic expansions, then discuss the rigorous two-scale convergence method as well as the Bloch wave decomposition. Eventually these tools will be apply to the Schrodinger equation with a periodic potential perturbed by a small macroscopic potential. The notion of effective mass for the one electron model in solid state physics will be derived. Localization effects will also be considered