An Algebraic q-Deformed Form for Shape-Invariant Systems
A.N.F. Aleixo (Rio de Janeiro Federal U.), A.B. Balantekin (Wisconsin, U., Madison), M.A. Candido Ribeiro (Sao Paulo, IFT)
TL;DR
This paper introduces a quantum deformed algebraic framework for shape-invariant systems, extending classical potentials like Morse, Scarf, and Coulomb with new q-deformed ladder operators that preserve shape-invariance.
Contribution
It develops a novel q-deformed algebraic approach for shape-invariant systems, including new ladder operators and generalized potentials.
Findings
q-deformed ladder operators satisfy new commutation relations
Constructed q-deformed models preserve shape-invariance
Provided examples with Morse, Scarf, and Coulomb potentials
Abstract
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserve the shape-invariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and Coulomb potentials are given as examples.
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