121 citations · 304 across the 7 of their papers we have counts for
5 papers · 1 filter
Integrable and superintegrable quantum systems in a magnetic field
Josee Berube, Pavel Winternitz
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermi…
Separation of variables and Lie algebra contractions. Applications to special functions
George Pogosyan, Alexey Sissakian, Pavel Winternitz
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
Superintegrable Systems in Darboux spaces
E. G. Kalnins, J. M. Kress, W. Miller +1
Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four…
Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
Decio Levi, Piergiulio Tempesta, Pavel Winternitz
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The m…
Discrete matrix Riccati equations with superposition formulas
Alexei V. Penskoi, Pavel Winternitz
An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinea…