Multiseparability and superintegrability for classical and quantum systems (Q2709056)

The concept of a ``nondegenerate potential'' is applied to the study of superintegrable classical and quantum mechanical systems. Each system is associated with a pair of constants of a motion in the classical case and a pair of symmetry operators in the quantum case, that generate a quadratic algebra. It is shown that there is a one-to-one correspondence between superintegrable systems and free-field symmetry operators that generate quadratic algebras. Examples of such systems are given and it is indicated how the superintegrability can be used to study the corresponding bound states. It is proven that the superintegrability implies multiseparability. Details are given for the case of two-dimensional complex Euclidean space. It is suggested that the results obtained in this paper can be extended to higher dimensional systems.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00031].