%0 Journal Article
%T The relativistic Scott correction for atoms and molecules
%A Jan Philip Solovej
%A Thomas £¿stergaard S£¿rensen
%A Wolfgang L. Spitzer
%J Mathematics
%D 2008
%I arXiv
%X 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 [Sorensen], as well as the correction given here are of semi-classical nature. Our result on atoms and molecules is proved from a general semi-classical estimate for relativistic operators with potentials with Coulomb-like singularities. This semi-classical estimate is obtained using the coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a unified treatment of the relativistic as well as the non-relativistic case.
%U http://arxiv.org/abs/0808.2163v1