Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass

The bound-state solutions and the su(1,1) description of the d -dimensional radial harmonic oscillator, the Morse, and the D -dimensional radial Coulomb Schrödinger equations are reviewed in a unified way using the point canonical transformation method. It is established that the spectrum generating su(1,1) algebra for the first problem is converted into a potential algebra for the remaining two. This analysis is then extended to Schrödinger equations containing some position-dependent mass. The deformed su(1,1) construction recently achieved for a d -dimensional radial harmonic oscillator is easily extended to the Morse and Coulomb potentials. In the last two cases, the equivalence between the resulting deformed su(1,1) potential algebra approach and a previous deformed shape invariance one generalizes to a position-dependent mass background a well-known relationship in the context of constant mass. © 2008 American Institute of Physics.SCOPUS: ar.j