Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation

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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 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 figures

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Exactly Solvable and Integrable Systems, High Energy Physics - Lattice, High Energy Physics - Theory, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/80486

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0305047
 http://arxiv.org/abs/nlin/0305047
 J.Math.Phys. 45 (2004) 4077-4105
 doi:10.1063/1.1780612

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arXiv