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.

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 cc and bottomonium bb; in both ordinary nonrelativistic quantum mechanics symmetries and three-dimensional nonrelativistic noncommutative 3D-NRNCQM symmetries. [ABSTRACT FROM AUTHOR]