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

  • Andrew HassellEmail author
  • 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, 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.

Key words and phrases

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

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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