Asymptotics of the ground state energy in the relativistic settings and with self-generated magnetic field

Andrew Hassell () and Victor Ivrii ()
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Andrew Hassell: University of Toronto, Department of Mathematics
Victor Ivrii: University of Toronto, Department of Mathematics

Chapter Chapter 33 in Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 2019, pp 559-581 from Springer

Abstract: Abstract The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. Also we will prove that 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; Self-generated Magnetic Field; 35P20; 81Q10 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-30561-1_33

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DOI: 10.1007/978-3-030-30561-1_33

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