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 …

The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a
Hamiltonian constructed from the combination of two independent parabosonic oscillators …

We present all real quantum mechanical potentials in a two-dimensional Euclidean space
that have the following properties: 1. They allow separation of variables of the Schrödinger …

An algebraic interpretation of the bivariate Krawtchouk polynomials is provided in the
framework of the three-dimensional isotropic harmonic oscillator model. These polynomials …

Two Dunkl oscillator models are considered: one singular and the other with a 2: 1
frequency ratio. These models are defined by Hamiltonians which include the reflection …

The multivariate Meixner polynomials are shown to arise as matrix elements of unitary
representations of the SO (d, 1) group on oscillator states. These polynomials depend on d …

An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms
of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk …

A finite oscillator model based on two-variable Krawtchouk polynomials is presented and its
application to spin dynamics is discussed. The model is defined on a triangular lattice. The …

In this paper we deal with limit relations between bivariate hypergeometric polynomials. We
analyze the limit relation from trinomial distribution to bivariate Gaussian distribution …

The quantum state transfer properties of a class of two-dimensional spin lattices on a
triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly …