Some properties of the potential-to-ground state map in quantum mechanics (Q2050076)

The author considers properties of the map from potential to the ground state in many-body quantum mechanics. External potentials \(v\in L^p + L^\infty\) and interaction potentials \(w \in L^p + L^\infty\) for \(p> \max(2d/3, 2)\) where \(d\) is the dimension of the underlying space are considered. The first result is that the space of binding potentials is path-connected. Then the author shows that the map from potentials to the ground state is locally weak-strong continuous and that its differential is compact. This implies that the Kohn-Sham inverse problem in Density Functional Theory is ill-posed on a bounded set.