Estimates on derivatives of Coulombic wave functions and their electron densities

Søren Fournais, Thomas Østergaard Sørensen*

*Corresponding author af dette arbejde

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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 p, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.

OriginalsprogEngelsk
TidsskriftJournal fur die Reine und Angewandte Mathematik
Vol/bind2021
Nummer775
ISSN0075-4102
DOI
StatusUdgivet - jun. 2021

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