Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation

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dc.creatorLevi, Decio
dc.creatorTempesta, Piergiulio
dc.creatorWinternitz, Pavel
dc.date2003-05-23
dc.date.accessioned2026-07-07T05:34:45Z
dc.date.available2026-07-07T05:34:45Z
dc.descriptionWe 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.
dc.description41 pages, no figures
dc.identifierhttps://arxiv.org/abs/nlin/0305047
dc.identifierhttp://arxiv.org/abs/nlin/0305047
dc.identifierJ.Math.Phys. 45 (2004) 4077-4105
dc.identifierdoi:10.1063/1.1780612
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80486
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleUmbral Calculus, Difference Equations and the Discrete Schroedinger Equation
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