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Abstract

In present work, the modified Schrödinger equation (MSE) is analytically solved. The Heavy-Light Mesons (HLM) under modified nonrelativistic quark-antiquark potential, are extended to the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp's shift method. The energy a spectrum of HLM has been investigated in the framework of the perturbative quantum chromodynamics (PQCD) extended nonrelativistic quark model. The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. The masses of the scalar, vector, pseudoscalar, and pseudovector for (B, Bs, D and Ds) mesons have been calculated in (NC: 3D-RSP). Moreover, using the perturbation approach, we found that the perturbative solutions of discrete spectrum can be expressed by the parabolic cylinder functions function 0 Gamma function (v), the discreet √22 atomic quantum numbers (j, 1, s, m) of the QQ state and (the spin independent and spin dependent) parameters (a, b, g, h), in addition to noncommutativity parameters (and). Furthermore, we have shown that the total complete degeneracy of new energy levels of HLM was changed to become equals to the new value 3n² instead to the old values n² in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCQM.

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