|
This article is cited in 10 scientific papers (total in 10 papers)
Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Juan A. Calzada, Javier Negro, Mariano A. del Olmo University of Valladolid
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.
Keywords:
superintegrable systems; intertwining operators; dynamical algebras.
Received: November 14, 2008; in final form March 18, 2009; Published online April 1, 2009
Citation:
Juan A. Calzada, Javier Negro, Mariano A. del Olmo, “Intertwining Symmetry Algebras of Quantum Superintegrable Systems”, SIGMA, 5 (2009), 039, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma385 https://www.mathnet.ru/eng/sigma/v5/p39
|
Statistics & downloads: |
Abstract page: | 438 | Full-text PDF : | 34 | References: | 33 |
|