Metamorphosis and duality between quantum systems

We show that a duality transformation (connecting integrable Hamiltonian systems) recently discovered by Hietarinta and co-workers in two dimensions at a classical level can be directly established in N dimensions from a quantum formulation of the problem. Further, we show duality to be valid for a much larger class of dynamical systems and to be not necessarily unique. We speculate that this nonuniqueness could be a characteristic of separable systems.