Lieb, Elliott H. Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion. (English) Zbl 0514.35074 Commun. Math. Phys. 85, 15-25 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 10 Documents 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) Keywords:Thomas-Fermi-von Weizsäcker equation; infinite atom without electron repulsion; uniqueness; positive solution × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adams, R.A.: Sobolev spaces. New York: Academic Press 1975 · Zbl 0314.46030 [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 D. thesis, Princeton University 1979 (unpublished) [3] Benguria, R., Brezis, H., Lieb, E.H.: The Thomas-Fermi-von Weizsäcker theory of atoms and molecules.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 · doi:10.1007/BF01942059 [4] Fermi, E.: Un metodo statistico per la determinazione di alcune priorieta dell’atome. Rend. Accad. Naz. Lincei6, 602–607 (1927) [5] Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0361.35003 [6] Kato, T.: On the eigenfunctions of many particle systems in quantum mechanics. Commun. Pure Appl. Math.10, 151–171 (1957) · Zbl 0077.20904 · doi:10.1002/cpa.3160100201 [7] Kato, T.: Schrödinger operators with singular potentials. Isr. J. Math.13, 135–148 (1973) · Zbl 0246.35025 · doi:10.1007/BF02760233 [8] Liberman, D., Lieb, E.H.: Numerical calculation of the Thomas-Fermi-von Weizsäcker function for an infinite atom without electron repulsion, Los Alamos National Laboratory report (in preparation) [9] Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys.53, 603–641 (1981) · Zbl 1114.81336 · doi:10.1103/RevModPhys.53.603 [10] Lieb, E.H., Simon, B.: The Thomas-Fermi theory of atoms, molecules, and solids. Adv. Math.23, 22–116 (1977) · Zbl 0938.81568 · doi:10.1016/0001-8708(77)90108-6 [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 [13] Thomas, L.H.: The calculation of atomic fields. Proc. Camb. Phil. Soc.23, 542–548 (1927) · JFM 53.0868.04 · doi:10.1017/S0305004100011683 [14] von Weizsäcker, C.F.: Zur Theorie der Kernmassen. Z. Phys.96, 431–458 (1935) · Zbl 0012.23501 · doi:10.1007/BF01337700 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.