General Nth-order superintegrable systems separating in polar coordinates


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

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.51, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 40
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1088/1751-8121/aadc23
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Özet

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.