Inverse generators in the algebraic description of quantum confined systems: Properties and connections with nonlinear quantum deformation process and phase operators

Abstract

We introduce, via their action on the eigenstate basis, the inverse or the one-sided inverse of the algebraic generators for a class of important potentials used to model quantum confined systems in several fields of physics. We obtain the complete algebraic formulation of the systems with the inclusion of the inverse generators. We establish the relations of this complete algebraic approach with the nonlinear quantum deformation approach and the generalization of the phase operators’ definition for these systems. We outline extensions for all the results obtained in this study for the case of the two-parameter quantum deformed systems which preserves the algebraic nature of the undeformed systems.