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, vol.50, no.7, pp.2067-2073, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 7
  • Publication Date: 2011
  • Doi Number: 10.1007/s10773-010-0572-2
  • Journal Name: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2067-2073
  • Keywords: Integrable systems, Intertwining operators, ISOSPECTRAL POTENTIALS, WINTERNITZ SYSTEM, HYPERBOLIC PLANE, 2 DIMENSIONS, SPHERE, OSCILLATOR
  • Ankara University Affiliated: Yes

Abstract

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.