Journal of Nanosciences: Current Research

A New Asymptotic Study to the 3-Dimensional Radial Schrodinger Equation under Modified Quark-antiquark Interaction Potential

Abstract

Abdelmadjid Maireche

In present work, the modified 3-dimensional modified radial Schrödinger equation is analytically solved for the nonrelativistic interactions under the modified quark-antiquark interaction potential in the symmetries of Non-Commutative Quantum Mechanics (NCQM), using the generalized Bopp’s shift method in the case of perturbed Non-Relativistic Quantum Chromodynamics (pNRQCD). The new energy eigenvalues (ground state, first excited state and nth excited state) and the corresponding Hamiltonian operator are calculated in 3-dimensional Non-Commutative Real Space Phase (NC: 3D-RSP) symmetries instead of solving modified Schrödinger Weyl Moyal star product. The present results, in (NC: 3D-RSP), are applied on the charmonium , bottomonium and mesons. It is found that the perturbative solutions of discrete spectrum and quarkoniums mass can be expressed by the the parabolic cylinder functions function, Gamma function, the discreet atomic quantum numbers ( j, l, s, m) of the state and the potential parameters (a,b,c), in addition to non-commutativity parameters ( Θ and ). The total complete degeneracy of new energy levels of the modified quark-antiquark interaction potential changed to become equals to the value 3n2 instead the values n² in ordinary Commutative Quantum Mechanics (CQM). Our obtained results are in good agreement with the already existing literatures in NCQM.