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Abstract: In this paper we present the first steps for obtaining a discrete QuantumMechanics making use of the Umbral Calculus. The idea is to discretize thecontinuous Schroedinger equation substituting the continuous derivatives bydiscrete ones and the space-time continuous variables by well determinedoperators that verify some Umbral Calculus conditions. In this way we assurethat some properties of integrability and symmetries of the continuous equationare preserved and also the solutions of the continuous case can be recovereddiscretized in a simple way. The case of the Schroedinger equation with apotential depending only in the space variable is discussed.

Author: E. Lopez-Sendino, J. Negro, M. A. del Olmo, E. Salgado

Source: https://arxiv.org/

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