Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials
Mathematical Physics
2019-02-20 v2 math.MP
Abstract
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordinates and admit an independent fourth-order integral of motion. The general form of the potentials satisfies a linear ODE. In the classical case, the standard potentials coincide with the Tremblay-Turbiner-Winternitz (TTW) or Post-Winternitz (PW) models. In the quantum case new superintegrable systems are obtained, in addition to the TTW and PW ones. Their classical limit is free motion.
Cite
@article{arxiv.1804.05751,
title = {Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials},
author = {A. M. Escobar-Ruiz and J. C. López Vieyra and P. Winternitz and I. Yurdusen},
journal= {arXiv preprint arXiv:1804.05751},
year = {2019}
}
Comments
30 pages