Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems

Abstract: We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\"odinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.