Heavy quarkonium systems for the deformed unequal scalar and vector Coulomb-Hulthén potential within the deformed effective mass Klein-Gordon equation using the improved approximation of the centrifugal term and Bopp’s shift method in RNCQM symmetries. (English) Zbl 07822286
Summary: In this study, the analytical solutions of the Klein-Gordon equation for any \(l\) states of the modified effective mass potential under the modified unequal scalar and vector Coulomb-Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions for eigenvalues of the energy spectrum and the new mass of mesons, such as charmonium and bottomonium that have the quark and antiquark flavor, have been estimated by using Bopp’s shift method, and perturbation theory. The energy state equation depends on the global parameters characterizing the noncommutativity space and the potential parameter \((v_0, s_0, v_1, s_1, m_0, m_1, \delta)\) in addition to the Gamma function and the discreet atomic quantum numbers \((j, l, s, m)\). The expression for the new energy spectra is applied to obtain the new mass spectra of heavy quarkonium systems (charmonium and bottomonium) in the symmetries of (RNC: 3D-RS). The comparisons show that our theoretical results are in very good agreement with the reported works.
MSC:
| 81R60 | Noncommutative geometry in quantum theory |
| 81S10 | Geometry and quantization, symplectic methods |
| 53D55 | Deformation quantization, star products |
| 11M55 | Relations with noncommutative geometry |
| 14A22 | Noncommutative algebraic geometry |
| 81T75 | Noncommutative geometry methods in quantum field theory |
Keywords:
Klein-Gordon equation; Hulthén potential; Coulomb potential; quark-antiquark; noncommutative geometry; deformation quantization; star productsReferences:
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