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Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion. (English) Zbl 0514.35074


MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[2] Benguria, R.: The von Weizsäcker and exchange corrections in Thomas-Fermi theory. Ph. D. thesis, Princeton University 1979 (unpublished)
[3] Benguria, R., Brezis, H., Lieb, E.H.: The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Commun. Math. Phys.79, 167–180 (1981) · Zbl 0478.49035
[4] Fermi, E.: Un metodo statistico per la determinazione di alcune priorieta dell’atome. Rend. Accad. Naz. Lincei6, 602–607 (1927)
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[9] Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys.53, 603–641 (1981) · Zbl 1114.81336
[10] Lieb, E.H., Simon, B.: The Thomas-Fermi theory of atoms, molecules, and solids. Adv. Math.23, 22–116 (1977) · Zbl 0938.81568
[11] Morrey, C.B., Jr.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[12] Stampacchia, G.: Equations elliptiques du second ordre à coefficients discontinus. Montréal: Presses de l’Univ. 1965 · Zbl 0151.15401
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[14] von Weizsäcker, C.F.: Zur Theorie der Kernmassen. Z. Phys.96, 431–458 (1935) · Zbl 0012.23501
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