Asymptotic behavior of the generalized quantum mechanical two Coulomb centers problem

Abstract

In this paper, we obtain asymptotic formulas for the eigenfunctions and terms of the quantum generalized problem of two Coulomb centers. For this purpose, we used the quasiclassical approximation, perturbation theory, and the method of reference equations. It is shown that results of different methods in asymptotic regions R → 0 and R →∞ are in a good agreement with each other. An interesting effect of the degeneration of the energy spectrum with an increase in the inter-center distance parameter R is obtained. Possible applications in physics are related to the description of one-electron states in potential models which take into account the 3D-structure of nano-objects of a ring-like and spheroidal shape as well as Rydberg-like states of electrons in ring molecules.