Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
Exactly Solvable and Integrable Systems
2007-05-23 v1 High Energy Physics - Lattice
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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 Schr\"{o}dinger 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.
Cite
@article{arxiv.nlin/0305047,
title = {Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation},
author = {Decio Levi and Piergiulio Tempesta and Pavel Winternitz},
journal= {arXiv preprint arXiv:nlin/0305047},
year = {2007}
}
Comments
41 pages, no figures