Journal of Physical Studies 25(1), Article 1002 [12 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.1002

BOUND-STATE SOLUTIONS OF THE MODIFIED KLEIN–GORDON AND SCHRÖDINGER EQUATIONS FOR ARBITRARY L-STATE WITH THE MODIFIED MORSE POTENTIAL IN THE SYMMETRIES OF NONCOMMUTATIVE QUANTUM MECHANICS

Abdelmadjid Maireche 

Laboratory of Physics and Material Chemistry, Physics department, Sciences Faculty, University of M'sila,
BP 239 Chebilia-M'sila, Algeria
e-mail: abdelmadjid.maireche@univ-msila.dz

Received 08 May 2020; in final form 27 November 2020; accepted 03 December 2020; published online 23 February 2021

In this work, approximate analytical solutions of both modified Klein-Gordon equation and Schrödinger equation in noncommutative relativistic and nonrelativistic three-dimensional real space have been explored by using the Pekeris approximation scheme to deal with the centrifugal term, Bopp's shift method and standard perturbation theory. We present the bound-state energy equation with a newly proposed potential called the modified Morse potential under the condition of equal scalar and vector potentials. The potential is a superposition of the Morse potential and some exponential radial terms. The aim of combining these potentials is to have an extensive application. We show that the new energy depends on the global parameters ($Θ^{c}$ and $σ^{c}$) characterizing the noncommutativity space-space and the potential parameter ($D_{e},r_{e},α$) in addition to the Gamma function and the discreet atomic quantum numbers $(j,l,s,m)$. The present results are applied in calculating both the energy spectrum for a few heterogeneous (LiH, HCl, NO) and homogeneous (H$_{2}$, I$_{2}$, O$_{2}$) diatomic molecules. We have also discussed some special cases of physical importance.

Key words: Klein–Gordon equation, Schrödinger equation, the Morse potential, noncommutative quantum mechanics, star products

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