×

On some basic properties of density functionals for angular momentum channels. (English) Zbl 0644.46059

Summary: We investigate some basic properties of the Hellmann and the Hellmann- Weizsäcker energy functional, density functionals, which use densities for angular momentum channels as trial functions, and investigate their relation to the ground state energy of an atomic N-electron system. Furthermore, various scaling properties are shown, the virial theorem, and in the case of no electron-electron interaction the dependence on the nuclear charge.

MSC:

46N99 Miscellaneous applications of functional analysis
81V10 Electromagnetic interaction; quantum electrodynamics
82B10 Quantum equilibrium statistical mechanics (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Thomas, L. H., Proc. Camb. Philos. Soc., 23, 542-548 (1927)
[2] Fermi, E., Rend. Accad. Naz. Lincei, 6, 602-607 (1927)
[3] Lenz, W., Z. Phys., 77, 713-721 (1932)
[4] March, N. H., Adv. in Phys., 6, 1-101 (1957)
[5] Lieb, E. H.; Simon, B., Adv. Math., 23, 22-116 (1977)
[6] Lieb, E. H., Rev. Mod. Phys., 53, 603-641 (1981)
[7] Thirring, W., Commun. Math. Phys., 79, 1-7 (1981)
[8] Scott, J. M.C., Phil. Mag., 43, 859-867 (1952)
[9] Schwinger, J., Phys. Rev., A22, 1827-1832 (1980)
[10] Schwinger, J.; Englert, B. G., Phys. Rev., A29, 2331-2338 (1984)
[11] Hellmann, H., Acta Physicochemica URSS, 4, 225-244 (1936)
[12] Siedentop, H. K.H., Z. Phys., A302, 213-218 (1981)
[13] Lieb, E. H.; Thirring, W. E., Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev Inequalities, (Lieb, E. H.; Simon, B.; Wightman, A. S., Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann (1976), Princeton University Press: Princeton University Press Princeton) · Zbl 0342.35044
[14] Sölter G.U.: private communication.; Sölter G.U.: private communication.
[15] Adams, R. A., Sobolev Spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101
[16] Benguria, R.; Brezis, H.; Lieb, E. H., Commun. Math. Phys., 79, 167-180 (1981)
[17] Lieb, E. H., Phys. Rev. Lett., 47, 69 (1981)
[18] Siedentop, H. K.H.; Weikard, R., Abh. Braunschweig. Wiss. Ges. (Germany), 38, 145-158 (1986)
[19] Siedentop H.K.H. and Weikard R.: On the leading energy correction for the statistical model of the atom: Interacting caseCommun. Math. Phys.; Siedentop H.K.H. and Weikard R.: On the leading energy correction for the statistical model of the atom: Interacting caseCommun. Math. Phys. · Zbl 0925.35125
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.