Heisenberg-type higher order symmetries are studied for both classical and
quantum mechanical systems separable in cartesian coordinates. A few particular
cases of this type of superintegrable systems were already considered in the
literature, but here they are characterized in full generality together with
their integrability properties. Some of these systems are defined only in a
region of Rn, and in general they do not include bounded solutions.
The quantum symmetries and potentials are shown to reduce to their
superintegrable classical analogs in the ââ0 limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit