Umbral calculus, difference equations and the discrete Schrödinger equation

  title={Umbral calculus, difference equations and the discrete Schr{\"o}dinger equation},
  author={D. Levi and P. Tempesta and P. Winternitz},
  journal={Journal of Mathematical Physics},
In this paper, we 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 Schrodinger 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… Expand
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