The relativistic Scott correction for atoms and molecules

TY - JOUR

T1 - The relativistic Scott correction for atoms and molecules

AU - Solovej, Jan Philip

AU - Sørensen, Thomas Østergaard

AU - Spitzer, Wolfgang L.

PY - 2010/1

Y1 - 2010/1

N2 - 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 [25], 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 [36]. The paper contains a unified treatment of the relativistic as well as the nonrelativistic case.

AB - 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 [25], 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 [36]. The paper contains a unified treatment of the relativistic as well as the nonrelativistic case.

M3 - Journal article

SN - 0010-3640

VL - 63

SP - 39

EP - 118

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 1

ER -