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Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Physics Department, Cinvestav, Apdo. postal 14-740, 07300 Mexico City, Mexico
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Symmetry 2017, 9(10), 217; https://doi.org/10.3390/sym9100217
Received: 25 July 2017 / Revised: 30 August 2017 / Accepted: 2 September 2017 / Published: 7 October 2017
We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations. View Full-Text
Keywords: discrete quantum mechanics; self-adjoint operators; exact finite differences; momentum operator; non equally spaced mesh points, translations discrete quantum mechanics; self-adjoint operators; exact finite differences; momentum operator; non equally spaced mesh points, translations
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Martínez-Pérez, A.; Torres-Vega, G. Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions. Symmetry 2017, 9, 217.

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