The one-dimensional Kepler-Coulomb problem on the space with constant curvature George Pogosyan
(pogosyan@fis.unam.mx or
pogosyan@thsun1.jinr.ru) Abstract In this paper we have constracted the mapping of S$_{1C}\to$S$_1$ and H$_1\to H$_1$ which are generalize the well known from Euclidean space one-dimensional type of Hurwitz transformations. We have shown, that as in the case of flat space this transformation permit one to establish the correspondence between Coulomb and oscillator problem with additional Calogero-Sutherland potential. We have seen that using this generalized transformation we can completely solved the quantum Coulomb problem on one dimensional sphere, and hyperboloid including eigenfunctions with correct normalization constant and energy spectrum. |