2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80486We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schrödinger equation in order to obtain a realization of nonrelativistic quantum mechanics in discrete space-time. In this approach a quantum system on a lattice has a symmetry algebra isomorphic to that of the continuous case. Moreover, systems that are integrable, superintegrable or exactly solvable preserve these properties in the discrete case.41 pages, no figuresExactly Solvable and Integrable SystemsHigh Energy Physics - LatticeHigh Energy Physics - TheoryMathematical Physicstext