Bulg. J. Phys. vol.50 no.1 (2023), pp. 054-075

The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

Abdelmadjid Maireche
Laboratory of Physics and Material Chemistry, Physics Department, Sciences Faculty, University of M'sila, P.O.B. 239, CHEBILIA M'sila, Algeria
Abstract. The analytical solutions of the mass-dependent Klien-Gordon equation (KGE) with the improved harmonic oscillator potential and the improved vector quark-antiquark interaction are derived from the symmetries of three-dimensional relativistic noncommutative quantum mechanics (3D-RNCQM symmetries) using Bopp's shift method and perturbation theory. The energy state equations are sensitive to the global parameters characterizing the noncommutativity space-space (Θ, σ) and the potential parameter (Enl, a, b, c, m0, k) in addition to the discrete atomic quantum numbers (j,l,s,m). The energy spectra for the mass-dependent Shrödinger equation with improved vector quark-antiquark interaction and harmonic oscillator potential were found using nonrelativistic limit principles. We also used the current findings to determine the heavy-meson masses of charmonium cc̅ and bottomonium bb̅ ; in both ordinary nonrelativistic quantum mechanics symmetries and three-dimensional nonrelativistic noncommutative 3D-NRNCQM symmetries.

doi: https://doi.org/10.55318/bgjp.2023.50.1.054

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