224 citations · 2.5k across the 74 of their papers we have counts for
8 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.
Lorentz and Galilei Invariance on Lattices
Decio Levi, Piergiulio Tempesta, Pavel Winternitz
We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. T…
Symmetries of Discrete Systems
Pavel Winternitz
In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie p…
Continuous symmetries of Lagrangians and exact solutions of discrete equations
Vladimir Dorodnitsyn, Roman Kozlov, Pavel Winternitz
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei inva…
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…