Abstract
LetE(R), respectivelye(R), denote the total energy, respectively the electronic contribution to the energy, in the Thomas-Fermi theory for a system of two fixed nuclei a distanceR apart. We prove thate(R) and −E(R) increase asR does. For the case ofN fixed nuclei, we prove the monotonicity ofe andE under certain displacements of the coordinates of the nuclei. The analogous result for the electronic contribution to the Born-Oppenheimer energy is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lieb, E.H., Simon, B.: Advan. Math.23, 22–116 (1977)
Teller, E.: Rev. Mod. Phys.34, 627–631 (1962)
Benguria, R., Lieb, E.H.: Commun. Math. Phys.63, 193–218 (1978)
Narnhofer, H., Thirring, W.: Acta Phys. Aust.41, 281–297 (1975)
Lieb, E.H., Simon, B.: J. Phys. B11, L537–542 (1978)
Lieb, E.H., Brezis, H.: Commun. Math. Phys.65, 231–246 (1979)
Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. In: Proc. of the Conference on Rigorous Atomic and Molecular Physics, Erice, June, 1980
Brezis, H.: Some variational problems of the Thomas-Fermi type. In: Proc. Symp. Erice. New York: J. Wiley 1978
Hoffmann-Ostenhof, T.: J. Phys. A13, 417–424 (1980)
Adams, R.A.: Sobolev spaces. New York: Academic Press 1975
Author information
Authors and Affiliations
Additional information
Communicated by E. Lieb
Research supported by U.S. National Science Foundation under Grant MCS 80-17781
Rights and permissions
About this article
Cite this article
Benguria, R. Dependence of the Thomas-Fermi energy on the nuclear coordinates. Commun.Math. Phys. 81, 419–428 (1981). https://doi.org/10.1007/BF01209076
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01209076