Estimates on derivatives of Coulombic wave functions and their electron densities
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Estimates on derivatives of Coulombic wave functions and their electron densities. / Fournais, Søren; Sørensen, Thomas Østergaard.
In: Journal fur die Reine und Angewandte Mathematik, Vol. 2021, No. 775, 01.06.2021, p. 1-38.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 373181009