Analysis and Mathematical Physics

Ludwig-Maximilians-Universität München

Mathematical Institute

Theresienstr. 39

80333 Munich

Tel. +49 89 2180 4622


Research Group


Research focus: mathematical foundations, electronic systems, quantum many-body physics

Our research is centered on the rigorous mathematical study of properties of electron systems, mainly with Coulomb interaction. Specifically, we are mostly interested in atoms and molecules in the clamped-nuclei approximation. Selected topics are regularity of exact eigenstates, and of solutions of effective models, such as Hartree-Fock theory, and various questions in spectral asymptotics.The research pertains to both non-relativistic and certain (pseudo)relativistic systems.

One main field of interest is the precise description of the behaviour of exact eigenstates of the full N-particle problem at the singularities of the many-body potential, beyond Kato's Cusp Condition, and its consequences for the behaviour of the corresponding electron density.

Another related topic is the regularity of solutions when the non-relativistic kinetic energy is replaced with a (pseudo)relativistic one, expressed by a non-local operator given by Einstein's energy relation. Similar questions are being investigated for solutions to Hartree-Fock and other mean field models, in both the non-relativistic and relativistic case.

Another field of interest is the study of various spectral asymptotics in the (pseudo)relativistic setting, both for Coulombic systems and for a (non-interaction) free electron gas in a bounded domain.


Estimates on derivatives of Coulombic wave functions and their electron densities

S. Fournais, T.Ø. Sørensen

Journal für die reine und angewandte Mathematik 775, 1-38 (2021).

Show Abstract

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.

DOI: 10.1515/crelle-2020-0047

Accept privacy?

Scroll to top