English

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.

Keywords

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

R2 v1 2026-06-23T01:25:04.272Z