Multiseparability and superintegrability in three dimensions

In complex two-dimensional Euclidean space, the Hamilton-Jacobi or Schrödinger equation with a given “nondegenerate” potential is maximally superintegrable if and only if it is separated in more than one coordinate system. A similar statement for three dimensions is not known. In this paper, a start will be made on this problem by investigating the known separable Hamilton-Jacobi and Schrödinger systems to find those that are superintegrable.