Estimates on derivatives of Coulombic wave functions and their electron densities

Author:

Fournais Søren1ORCID,Sørensen Thomas Østergaard2ORCID

Affiliation:

1. Department of Mathematics , Aarhus University , Ny Munkegade 118, DK-8000 Aarhus C , Denmark

2. Department Mathematisches Institut , LMU Munich , Theresienstr. 39, 80333 Munich , Germany

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference41 articles.

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5. A. Dall’Acqua, S. Fournais, T. Ø. Sørensen and E. Stockmeyer, Real analyticity away from the nucleus of pseudorelativistic Hartree–Fock orbitals, Anal. PDE 5 (2012), no. 3, 657–691.

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