How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements
Arkady L. Kholodenko
Abstract:Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 types of central potentials. These are of Kepler-Coulomb and harmonic oscillator type. Volker Perlick recently extended Bertrand theorem. He designed new static spherically symmetric (Bertrand) spacetimes obeying Einstein's equations and supporting closed orbits. In this work we demonstrate that the topology and geometry of these spacetimes permits us to solve quantum many-body problem for any atom of periodic system exactly. The computati… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.