Nth-Order superintegrable systems separating in polar coordinates


Yurduşen İ.

Geometry, Integrability and Quantization, vol.21, pp.334-348, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21
  • Publication Date: 2020
  • Doi Number: 10.7546/giq-21-2020-334-348
  • Journal Name: Geometry, Integrability and Quantization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.334-348
  • Keywords: Painleve property, separation of variables, superintegrability, ORDINARY DIFFERENTIAL-EQUATIONS, EVOLUTION-EQUATIONS, QUANTUM
  • Hacettepe University Affiliated: Yes

Abstract

© 2020 Bulgarian Academy of Sciences. All rights reserved.Classical and quantum Hamiltonian systems in two-dimensional Euclidean plane and allowing separation of variables in polar coordinates are investigated. The additional integral of motion is assumed to be a polynomial of degree N ≥ 3 in momenta. After analyzing the particular cases of N = 3, 4 and 5, a general description will be given. This leads to a classification of superintegrable potentials into two major categories. For the exotic potentials, the existence of an infinite family of superintegrable potentials in terms of the sixth Painlevé transcendent P6 is conjectured and will be demonstrated for the first few cases.