TY - JOUR

T1 - Estimates on derivatives of Coulombic wave functions and their electron densities

AU - Fournais, Søren

AU - Sørensen, Thomas Østergaard

N1 - Funding Information: This article may be reproduced in its entirety for non-commercial purposes. Søren Fournais was partially supported by a Sapere Aude Grant from the Independent Research Fund Denmark, Grant number DFF-4181-00221, and by the European Research Council, ERC grant agreement 202859. Thomas Østergaard Sørensen was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). Publisher Copyright: © De Gruyter 2021.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85105292022&partnerID=8YFLogxK

U2 - 10.1515/crelle-2020-0047

DO - 10.1515/crelle-2020-0047

M3 - Journal article

AN - SCOPUS:85105292022

VL - 2021

SP - 1

EP - 38

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 775

ER -