An Algebraic q-Deformed Form for Shape-Invariant Systems

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.