New exactly solvable systems with Fock symmetry

Abstract

New superintegrable systems are presented which, like the Hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One of them simulates a neutral fermion with non-trivial dipole moment, interacting with the external e.m. field. This system is presented in both non-relativistic and relativistic formulations. Another recently discovered system (see arXiv:1208.2886v1) is non-relativistic and includes the minimal and spin-orbit interaction with the external electric field. It is shown that all the considered systems are shape invariant. Applying this quality, these systems are integrated using the tools of SUSY quantum mechanics.