Some properties of the potential-to-ground state map in quantum mechanics
Mathematical Physics
2021-07-14 v2 Functional Analysis
math.MP
Spectral Theory
Quantum Physics
Abstract
We analyze the map from potentials to the ground state in static many-body quantum mechanics. We first prove that the space of binding potentials is path-connected. Then we show that the map is locally weak-strong continuous and that its differential is compact. In particular, this implies the ill-posedness of the Kohn-Sham inverse problem.
Keywords
Cite
@article{arxiv.2012.04054,
title = {Some properties of the potential-to-ground state map in quantum mechanics},
author = {Louis Garrigue},
journal= {arXiv preprint arXiv:2012.04054},
year = {2021}
}