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Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

Author

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  • Vasily E. Tarasov

    (Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

Abstract

An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.

Suggested Citation

  • Vasily E. Tarasov, 2016. "Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations," Mathematics, MDPI, vol. 4(3), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:44-:d:72932
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    References listed on IDEAS

    as
    1. Tarasov, Vasily E., 2015. "Lattice fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 12-33.
    2. Vasily E. Tarasov, 2015. "Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series," Journal of Mathematics, Hindawi, vol. 2015, pages 1-8, November.
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    Cited by:

    1. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.

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