224 citations · 2.5k across the 74 of their papers we have counts for
74 papers
Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
I. Yurdusen, O. O. Tuncer, P. Winternitz
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally i…
New infinite families of th-order superintegrable systems separating in Cartesian coordinates
A. M. Escobar-Ruiz, R. Linares, P. Winternitz
A study is presented of superintegrable quantum systems in two-dimensional Euclidean space allowing the separation of variables in Cartesian coordinates. In addition to the H…
Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
Ian Marquette, Pavel Winternitz
We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separatio…
Second-order delay ordinary differential equations, their symmetries and application to a traffic problem
Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko +1
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system c…
Two-dimensional superintegrable systems from operator algebras in one dimension
Ian Marquette, Masoumeh Sajedi, Pavel Winternitz
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start fro…
Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials
A. M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz +1
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordin…