Third order superintegrable systems separating in polar coordinates
Mathematical Physics
2015-05-18 v1 math.MP
Exactly Solvable and Integrable Systems
Classical Physics
Quantum Physics
Abstract
A complete classification is presented of quantum and classical superintegrable systems in that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function.
Keywords
Cite
@article{arxiv.1002.1989,
title = {Third order superintegrable systems separating in polar coordinates},
author = {Frederick Tremblay and Pavel Winternitz},
journal= {arXiv preprint arXiv:1002.1989},
year = {2015}
}