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arXiv · 0712.1965

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

C. Quesne
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Abstract

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.

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BibTeXRIS

C. Quesne. 2008-02-27. Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass. https://doi.org/10.1063/1.2838314

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