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, cilt.51, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 45
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1088/1751-8121/aae291
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Özet

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.