2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55441Using the underlying algebraic structures of Natanzon potentials, we discuss conditions that generate shape invariant potentials. In fact, these conditions give all the known shape invariant potentials corresponding to a translational change of parameters. We also find that while the algebra for the general Natanzon potential is $SO(2,2)$, a subgroup $SO(2,1)$ suffices for all the shape invariant problems of Natanzon type.LaTex file, 16 pages, Typographical errors and references correctedHigh Energy Physics - TheoryQuantum Physicstext