Intertwining Symmetry Algebras of Quantum Superintegrable Systems on Constant Curvature Spaces

Calzada J. A., KURU Ş., Negro J., del Olmo M. A.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, cilt.50, sa.7, ss.2067-2073, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 7
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1007/s10773-010-0572-2
  • Dergi Adı: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2067-2073
  • Anahtar Kelimeler: Integrable systems, Intertwining operators, ISOSPECTRAL POTENTIALS, WINTERNITZ SYSTEM, HYPERBOLIC PLANE, 2 DIMENSIONS, SPHERE, OSCILLATOR
  • Ankara Üniversitesi Adresli: Evet

Özet

A class of quantum superintegrable Hamiltonians defined on a hypersurface in a n+1 dimensional ambient space with signature (p,q) is considered and a set of intertwining operators connecting them are determined. It is shown that the intertwining operators can be chosen such that they generate the su(p,q) and so(2p,2q) Lie algebras and lead to the Hamiltonians through Casimir operators. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of some particular unitary representations.