2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57567We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relating eigenfunctions of {\emph three} different Hamiltonians is found, and some illustrative examples of the theory are analyzed, finding new potentials for which one eigenfunction and its corresponding eigenvalue is exactly known.Mathematical PhysicsHigh Energy Physics - TheoryQuantum Physicstext