Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
arXiv:0712.1965 · doi:10.1063/1.2838314
Abstract
The bound-state solutions and the su(1,1) description of the -dimensional radial harmonic oscillator, the Morse and the -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 -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.
arXiv comment24 pages, no figure, small change in introduction, one more reference, published version
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