A superintegrable system is, roughly speaking, a system that allows more integrals of motion
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …

The general description of superintegrable systems with one polynomial integral of order N
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …

The general form of an integral of motion that is a polynomial of order N in the momenta is
presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and …

We develop our method to prove quantum superintegrability of an integrable 2D system,
based on recurrence relations obeyed by the eigenfunctions of the system with respect to …

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb
systems, replacing their angular degrees of freedom by those of a generalized rational …

We show that the symmetry operators for the quantum superintegrable system on the 3-
sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly …

In this paper, we derive a nonseparable quantum superintegrable system in 2D real
Euclidean space. The Hamiltonian admits no second-order integrals of motion but does …

We review recent results on superintegrable quantum systems in a two-dimensional
Euclidean space with the following properties. They are integrable because they allow the …

The higher order superintegrability of separable potentials is studied. It is proved that these
potentials possess (in addition to the two quadratic integrals) a third integral of higher order …