A Theoretical Investigation of Time-Dependent Kohn--Sham Equations

Abstract

In this work, the existence, uniqueness, and regularity of solutions to the time-dependent Kohn--Sham equations are investigated. The Kohn--Sham equations are a system of coupled nonlinear Schrödinger equations that describe multiparticle quantum systems in the framework of the time-dependent density functional theory. In view of applications to control problems, the presence of a control function and the case of an inhomogeneity are also discussed.