The relativistic Scott correction for atoms and molecules
Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 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 [Sore...
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Zusammenfassung: | Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 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. |
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DOI: | 10.48550/arxiv.0808.2163 |