121 citations · 304 across the 7 of their papers we have counts for
10 papers
Quasiseparation of variables in the Schroedinger equation with a magnetic field
F. Charest, C. Hudon, P. Winternitz
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence…
A class of solvable Lie algebras and their Casimir Invariants
L. Snobl, P. Winternitz
A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their di…
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…