An upper bound on the ionic ground state density at the nucleus
type: Item
instance of: scholarly article
title: An upper bound on the ionic ground state density at the nucleus
zbMATH Open document ID: 0908.47064
DOI: 10.1016/0034-4877(96)82486-4
author: Natalja Rakowsky
author: Heinz Siedentop
published in: Reports on Mathematical Physics
publication date: 1997-11-13T00:00:00Z
review text: An upper bound on the electronic ground-state density of an \(N\)-electron Hamiltonian is proved. More precisely, it is shown that \[ \limsup_{Z\to\infty} {\rho_d(0)\over Z^3}\leq {\pi\over 48} q, \] where \(\rho_d\) is the corresponding density, \(Z\) is the charge of the nucleus and \(q\) is the number of spin states of a single electron. The authors provide a short proof for the above estimates which generalizes known results on neutral atoms. The main ingredients in the proof are an inequality of Hoffmann-Ostenhof et. al. for \(\rho_d(0)\) and Lieb-Thirring's estimate on the correlation energy.
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81V45
zbMATH DE Number: 1087267
zbMATH Keywords: upper bound
zbMATH Keywords: electronic ground-state density
reviewed by: André Noll
MaRDI profile type: Publication
full work available at URL: 0034-4877(96)82486-4
OpenAlex ID: W1967126132
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description: scientific article; zbMATH DE number 1087267