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, cilt.51, sa.40, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 40
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1088/1751-8121/aadc23
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: superintegrability, separation of variables, Painleve property, QUANTUM INTEGRABILITY, 3RD-ORDER INTEGRALS, HYDROGEN-ATOM, MECHANICS, SEARCH, MOTION, DRACH
  • Hacettepe Üniversitesi Adresli: Evet

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.