Abstract
New superintegrable systems are presented which, like the hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One system 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 Désilets et al 2012 arXiv:1208.2886v1) is non-relativistic and includes minimal and spin–orbit interaction with the external electric field. It is shown that all the systems considered are shape invariant. Applying this quality, these systems are integrated using the tools of SUSY quantum mechanics.
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