Number Theory and Atomic Densities
After the initial success to explain the hydrogen atom, one of the early challenges of quantum mechanics was to study larger atoms. The problems encountered in this process were numerous, and the quest for an understanding quickly became a search for simplified quantum atomic models that would explain different properties of the atom.
KeywordsAtomic Density Semiclassical Approximation Analytic Number Theory Large Atom Schrodinger Operator
Unable to display preview. Download preview PDF.
- [CFS2]Córdoba, A., Fefferman, C., Seco, L., “Weyl Sums and Atomic Energy Oscillations”, Revista Matemática Iberoamericana 11, no. 1, 167–228 (1995).Google Scholar
- [E]Englert, B.G., “Semiclassical Theory of the Atom”, Springer Verlag Lecture Notes in Physics 301.Google Scholar
- [FS5]Fefferman, C. and Seco, L., “The Eigenvalue Sum for a Three-Dimensional Radial Potential”, To appear in Adv. Math.Google Scholar
- [Fer]Fermi, E., “Un Metodo Statistico per la Determinazione di alcune Priorieta dell’Atome”, Rend. Accad. Naz. Lincei 6, 602–607 (1927).Google Scholar
- [GK]S.W. Graham and G. Kolesnik, “Van der Corput’s Method of Exponential Sums”, Cambridge University Press. London Math. Soc. Lecture Notes Series, 126.Google Scholar
- [ILS]A. Iantchenko, E. Lieb and H. Siedentop, “Proof of a Conjecture about Atomic and Molecular Cores Related to Scott’s Correction”, J. Reine u. Ang. Math. (in press).Google Scholar
- [L3]Lieb, E.H., “Atomic and Molecular Negative Ions”, Phys. Rev. Lett. 52, 315.Google Scholar
- [L4]Lieb, E.H., “Bound on the Maximum Negative Ionization of Atoms and Molecules”, Phys. Rev. A29, 3018–3028.Google Scholar
- [Sco]Scott, J.M.C., “The Binding Energy of the Thomas—Fermi Atom”, Phil. Mag. 43, 859–867 (1952).Google Scholar