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

Authors
  • Samary, Dine Ousmane1, 2
  • Guedezounme, Sêcloka Lazare1
  • Kanfon, Antonin Danvidé1
  • 1 University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), 072B.P.50, Cotonou, Republic of Benin , Cotonou (Benin)
  • 2 Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476, Potsdam, Germany , Potsdam (Germany)
Type
Published Article
Journal
Brazilian Journal of Physics
Publisher
Springer US
Publication Date
Apr 05, 2019
Volume
49
Issue
3
Pages
458–470
Identifiers
DOI: 10.1007/s13538-019-00655-8
Source
Springer Nature
Keywords
License
Yellow

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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