##### 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).

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.