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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 76–92 (Mi aa1596)

Research Papers

Asymptotics of the ground state energy in the relativistic settings

V. Ivrii

Department of Mathematics, University of Toronto, 40 St. George, St. Toronto, ON, M5S 2E4, Canada

Abstract: The paper is aimed at deriving sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, calculating the relativistic Scott correction term and also Dirac, Schwinger, and relativistic correction terms. Also it is proved that the Thomas–Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.

Keywords: relativistic Schrödinger operator, heavy atoms and molecules, Thomas–Fermi theory, Scott correction term, microlocal analysis, sharp spectral asymptotics.

 Funding Agency Grant Number Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN 13827 Supported in part by National Science and Engineering Research Council (Canada) Discovery Grant RGPIN 13827.

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Document Type: Article
Language: English

Citation: V. Ivrii, “Asymptotics of the ground state energy in the relativistic settings”, Algebra i Analiz, 30:3 (2018), 76–92

Citation in format AMSBIB
\Bibitem{Ivr18} \by V.~Ivrii \paper Asymptotics of the ground state energy in the relativistic settings \jour Algebra i Analiz \yr 2018 \vol 30 \issue 3 \pages 76--92 \mathnet{http://mi.mathnet.ru/aa1596} \elib{http://elibrary.ru/item.asp?id=32855065}