Abstract. A class of bound-state problems which represents the coupling of a three-level atom with a two-dimensional system involving two shape-invariant potentials was introduced in a previous paper. In this paper, we considered second-order parasupersymmetric quantum-mechanical models and two possible kinds for the coupling Hamiltonian (linear and nonlinear in the potential ladder operators). In the present paper, using an algebraic formulation for shape-invariant potential systems, we study the quantum dynamics of these coupled systems and obtain the temporal behaviour of some dynamical variables related with the atom and the coupling potentials. An application is given for a couple of shape-invariant potentials (Pöschl–Teller + self-similar potentials).

PACS numbers: 03.65.Ca, 03.65.Ge, 02.20.−a, 03.67.Mn

Print publication: Issue 29 (20 July 2007)
Received 18 April 2007, in final form 31 May 2007
Published 3 July 2007