Abstract
This article is a summary of what is know rigorously about Thomas-Fermi (TF) theory with and without the Dirac and von Weizsäcker corrections. It is also shown that TF theory agrees asymptotically, in a certain sense, with nonrelativistic quantum theory as the nuclear charge z tends to infinity. The von Weizsäcker correction is shown to correct certain undesirable features of TF theory and to yield a theory in much better agreement with what is believed (but as yet unproved) to be the structure of real atoms. Many open problems in the theory are presented.
This article appears in the Proceedings of the NATO Advanced Study Institute on Rigorous Atomic and Molecular Physics held at Erice in June, 1980, edited by G. Velo and A. S. Wightman, and published by Plenum Corporation. The present Rev. Mod. Phys. version contains corrections of some errors in the Plenum version.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-662-04360-8_51
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Lieb, E.H. (2001). Thomas-fermi and related theories of atoms and molecules. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_20
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