##### Estimates on derivatives of Coulombic wave functions and their electron densities

S. Fournais, T. O. Sørensen

Journal Fur Die Reine Und Angewandte Mathematik 775, 1-38 (2021).

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