Klein-Gordon Oscillator In Dynamical Noncommutative Space

This paper aims to investigate the two-dimensional Klein-Gordon oscillator system in a dynamical noncommutative (DNC) space. We address the deformed system using the time-independent perturbation theory, where the energy eigenvalues and eigenvectors are obtained in relativistic and nonrelativistic regimes, also the effects of the dynamical and non-dynamical noncommutative settings are successfully examined. Then some numerical results are given and used to extensively study the conduct of the system under the various considerations. Note that in the DNC space, the space-space commutation relations and noncommutative parameter are position-dependent. The first-order corrections to the eigensystem are found, then, it is shown that the energy shift depends on the DNC parameter tau\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}. Moreover, using the accuracy of energy measurement, we put an upper bound on the parameter tau\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}. Knowing that, with a set of two-dimensional Bopp-shift transformation, we link the noncommutative problem to the standard commutative one.