Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 039, 23 pages      arXiv:0904.0170      https://doi.org/10.3842/SIGMA.2009.039
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

Intertwining Symmetry Algebras of Quantum Superintegrable Systems

Juan A. Calzada a, Javier Negro b and Mariano A. del Olmo b
a) Departamento de Matemática Aplicada, Universidad de Valladolid, E-47011, Valladolid, Spain
b) Departamento de Física Teórica, Universidad de Valladolid, E-47011, Valladolid, Spain

Received November 14, 2008, in final form March 18, 2009; Published online April 01, 2009

Abstract
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness.

Key words: superintegrable systems; intertwining operators; dynamical algebras.

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