Relativistic Scott correction for atoms and molecules
Article first published online: 11 AUG 2009
Copyright © 2009 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 63, Issue 1, pages 39–118, January 2010
How to Cite
Solovej, J. P., Østergaard Sørensen, T. and Spitzer, W. L. (2010), Relativistic Scott correction for atoms and molecules. Comm. Pure Appl. Math., 63: 39–118. doi: 10.1002/cpa.20296
- Issue published online: 19 OCT 2009
- Article first published online: 11 AUG 2009
- Manuscript Received: NOV 2008
- Erwin Schrödinger Institute (Vienna, Austria)
- Department of Mathematics at the University of Copenhagen
- EU TMR
- Danish National Research Foundation
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in , as well as the correction given here, are of semiclassical nature. Our result on atoms and molecules is proved from a general semiclassical estimate for relativistic operators with potentials with Coulomb-like singularities. This semiclassical estimate is obtained using the coherent state calculus introduced in . The paper contains a unified treatment of the relativistic as well as the nonrelativistic case. © 2009 Wiley Periodicals, Inc.