Density functional theory (DFT) is one of the most used methods to model matter at microscopic scale in many-body quantum physics and chemistry. It can be expressed in terms of an inverse problem, linking electric potentials to one-body eigenstates densities corresponding to those potentials. We will introduce the main objects of DFT, present the uniqueness theorem of the subject, and we will show how to invert the map, theoretically and numerically, for ground and excited states.
https://indico.math.cnrs.fr/event/7688/