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Estimates on derivatives of Coulombic wave functions and their electron densities

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  • Søren Fournais
  • Thomas Østergaard Sørensen, Department Mathematisches Institut, Ludwig Maximilian University of Munich

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.

TidsskriftJournal fur die Reine und Angewandte Mathematik
StatusUdgivet - jun. 2021

Bibliografisk note

Funding Information:
This article may be reproduced in its entirety for non-commercial purposes. S?ren 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 ?stergaard S?rensen was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany?s Excellence Strategy (EXC-2111-390814868).

Publisher Copyright:
© De Gruyter 2021.

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