Dynamical algebras for Poschl-Teller Hamiltonian hierarchies

The dynamical algebras of the trigonometric and hyperbolic symmetric Poschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3,2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way. (C) 2009 Elsevier Inc. All rights reserved.