Abstract
One of the qualitative features of the periodic table is that all atoms have essentially the same size. More precisely, in each group of the periodic table the atomic radius is nearly constant. I shall in my lecture present a mathematical result, that, to some extent, explains this very important feature. In the spirit of the congress I will show how many branches of mathematics need to be united to understand the structure of large atoms. Among the tools I shall discuss are generalized Sobolev inequalities, semi- classical estimates, variational methods, and non-linear elliptic PDE.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Bach, Ionization energies of bosonic Coulomb systems, Lett. Math. Phys., 21, 139–149, (1991).
H. Brezis & E.H. Lieb, Long range potentials in Thomas-Fermi theory. Commun. Math. Phys., 65, 231–246, (1979).
C. Fefferman & L.A. Seco, Asymptotic neutrality of large ions. Commun. Math. Phys., 128, 109–130, (1990).
E.H. Lieb Thomas-Fermi and related theories of atoms and molecules, Rev. Modern Phys., 53, 603–641, (1981).
E.H. Lieb & B. Simon, The Hartree-Fock theory for Coulomb systems, Commun. — Math. Phys., 53, 185–194, (1977).
E.H. Lieb & B. Simon, Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math., 23, 22–116, (1977).
E.H. Lieb & W.E. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, in Studies in mathematical physics, (E. Lieb, B. Simon, and A.S. Wightman, Eds.), Princeton Univ. Press, Princeton, New Jersey, 269–330, 1976.
J.P. Solovej, Asymptotics for bosonic atoms. Lett. Math. Phys., 20, 165–172, 1990.
J.P. Solovej, Proof of the ionization conjecture in a reduced Hartree-Fock model, Invent. Math., 104, 291–311, (1991).
J.P. Solovej, The size of atoms in Hartree-Fock theory, in Partial Differential Equations and Mathematical Physics, Progress in Nonlinear Differential Equations and Their Applications, Vol. 21, L. Hörmander and A. Melin (Eds.), 321–332, Birkhäuser, (1995).
A. Sommerfeld, Asymptotische Integration der Differentialgleichung des Thomas-Fermischen Atoms,Z. Phys., 78, 283–308, (1932).
Hermann Weyl, Über die asymptotische Verteilung der Eigenwerte. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Naturwissenschaftliche Klasse, 110–117, 1911.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this paper
Cite this paper
Solovej, J.P. (1998). Mathematical Results on the Structure of Large Atoms. In: Balog, A., Katona, G.O.H., Recski, A., Sza’sz, D. (eds) European Congress of Mathematics. Progress in Mathematics, vol 169. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8898-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8898-1_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9819-5
Online ISBN: 978-3-0348-8898-1
eBook Packages: Springer Book Archive