Accidental degeneracies and tridimensional potentials

The problem of the search for three-dimensional potentials possessing higher (accidental) symmetries is examined in the framework of a classical Hamiltonian theory. Under suitable restrictions a class of potentials leading to strictly periodical motions has been found for each of the eleven Eisenhart co-ordinate systems. Further, the separated Schrodinger equations, written for the above classical potentials, have been classified.