Superintegrable Lissajous systems on the sphere

Creative Commons License

Calzada J. A., KURU Ş., Negro J.

EUROPEAN PHYSICAL JOURNAL PLUS, cilt.129, sa.8, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 129 Sayı: 8
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1140/epjp/i2014-14164-5
  • Dergi Adı: EUROPEAN PHYSICAL JOURNAL PLUS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Ankara Üniversitesi Adresli: Evet

Özet

The kind of systems on the sphere, whose trajectories are similar to the Lissajous curves, is studied by means of one example. The symmetries are constructed following a unified and straightforward procedure for both quantum and classical versions of the model. In the quantum case it is stressed how the symmetries give the degeneracy of each energy level. In the classical case it is shown how the constants of motion supply the orbits, the motion and the frequencies in a natural way. The associated sets of polynomial constants of motion and symmetries as well as their algebraic relations are also obtained and compared for the classical and quantum cases.