Zdenek Kabat (Czech Technical University in Prague, Czech Republic)

Umbral discretization of quantum systems

Abstract:
   We use the methods of umbral calculus for discretization of certain classes of superintegrable systems in the Euclidean plane. The discrete versions of gauge-rotated Hamiltonians lead to the polynomials different from the known orthogonal polynomials of a discrete variable. An infinite number of possible discretizations offers a way to obtain yet another polynomials.