Fourth-order superintegrable systems separating in polar coordinates. II. Standard potentials


Escobar-Ruiz A. M. , Lopez Vieyra J. C. , WINTERNITZ P., Yurdusen I.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.51, no.45, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 45
  • Publication Date: 2018
  • Doi Number: 10.1088/1751-8121/aae291
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
  • Keywords: superintegrability, separation of variables, standard potentials, higher order integrals of motion, CONFORMALLY FLAT SPACES, CLASSICAL STRUCTURE-THEORY, 3RD-ORDER INTEGRALS, STACKEL TRANSFORM, QUANTUM, SYMMETRIES, CLASSIFICATION, SEARCH, TTW

Abstract

Superintegrable Hamiltonian systems in a two-dimensional Euclidean space arc 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.