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Asymptotics of the Ground State Energy in the Relativistic Settings

  • Victor IvriiEmail author
Chapter

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, 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.

Key words and phrases

Relativistic Schrödinger operator Heavy atoms and Molecules Thomas-Fermi theory Scott correction term Microlocal Analysis Sharp Spectral Asymptotics 

2010 Mathematics Subject Classification:

35P20 81Q10 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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