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Lattice Oscillator Model on Noncommutative Space: Eigenvalues Problem for the Perturbation Theory

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Abstract

Harmonic oscillator in noncommutative two-dimensional lattice is investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding Hamiltonian. First, we consider the case of ordinary quantum mechanics, and we point out the thermodynamic properties of the model. Then we consider the same question when both coordinates and momenta are noncommutative.

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Acknowledgments

D.O.S research at the Max-Planck Institute is supported by the Alexander von Humboldt foundation. S.L.G thanks the Max-Planck Institute for the invitation and financial support.

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Authors and Affiliations

  1. International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072B.P.50, Cotonou, Republic of Benin

    Dine Ousmane Samary, Sêcloka Lazare Guedezounme & Antonin Danvidé Kanfon

  2. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476, Potsdam, Germany

    Dine Ousmane Samary

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  1. Dine Ousmane Samary
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Samary, D.O., Guedezounme, S.L. & Kanfon, A.D. Lattice Oscillator Model on Noncommutative Space: Eigenvalues Problem for the Perturbation Theory. Braz J Phys 49, 458–470 (2019). https://doi.org/10.1007/s13538-019-00655-8

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