General Nth-order superintegrable systems separating in polar coordinates

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Escobar-Ruiz A. M., Winternitz P., Yurdusen I.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.51, no.40, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 40
  • Publication Date: 2018
  • Doi Number: 10.1088/1751-8121/aadc23
  • Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: superintegrability, separation of variables, Painleve property, QUANTUM INTEGRABILITY, 3RD-ORDER INTEGRALS, HYDROGEN-ATOM, MECHANICS, SEARCH, MOTION, DRACH
  • Hacettepe University Affiliated: Yes

Abstract

The general description of superintegrable systems with one polynomial integral of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane. We consider classical and quantum Hamiltonian systems allowing separation of variables in polar coordinates. The potentials can be classified into two major classes and their main properties are described. We conjecture that a new infinite family of superintegrable potentials in terms of the sixth Painleve transcendent P-6 exists and demonstrate this for the first few cases.