Three-level coupled systems and parasupersymmetric shape invariance

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 is introduced. We consider second-order parasupersymmetric quantum-mechanical models and, using an algebraic formulation for shape-invariant potential systems, resolve the eigenvalue problem for these coupled systems considering two possible kinds for the coupling Hamiltonian (linear and nonlinear in the potential ladder operators). An application is given for a couple of shape-invariant potentials (harmonic oscillator + Morse potentials).