Lattice oscillator model on noncommutative space, eigenvalues problem for the 
perturbation theory

Guedezounme, Sêcloka Lazare; Kanfon, Antonin Danvidé; Ousmane Samary, Dine

doi:10.1007/s13538-019-00655-8

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Lattice oscillator model on noncommutative space, eigenvalues problem for the perturbation theory

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Ousmane Samary, Dine
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Guedezounme, S. L., Kanfon, A. D., & Ousmane Samary, D. (2019). Lattice oscillator model on noncommutative space, eigenvalues problem for the perturbation theory. Brazilian Journal of Physics, 49(3), 458-470. doi:10.1007/s13538-019-00655-8.

Cite as: https://hdl.handle.net/21.11116/0000-0000-74B2-4

Abstract

Harmonic oscillator in noncommutative two dimensional lattice are
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
momentums are noncommutative.