A theoretical investigation of nonrelativistic bound state solution at finite temperature using the sum of modified Cornell plus inverse quadratic potential

Abstract

New modified nonrelativistic bound state energy eigenvalues have been obtained for the hydrogenic atoms with spin ½ under the sum of modified Cornell plus inverse quadratic potential (MCIQP), at finite temperature, in the symmetries of the noncommutative three-dimensional real space phase (NC: 3D-RSP). The ordinary sum of Cornell plus inverse quadratic potential is extended by including new central terms to become MCIQP. In addition, MCIQP is suggested as a quark–antiquark interaction potential for studying the masses of heavy and heavy–light mesons in (NC: 3D-RSP), in which the potential satisfies the features of quantum chromodynamics theory of strong interaction. For this purpose, the modified radial Schrodinger equation is analytically solved using the generalized Bopp’s shift method and standard perturbation theory. The energy eigenvalues and the corresponding new Hamiltonian operator are obtained in (NC: 3D-RSP). These results are applied to calculate the mass of mesons such as charmonium, bottomoniumand mesons with spin (0 or 1). In a thermal medium of a positive temperature, the new parameters of the studied potential MCIQP become temperature dependent because of color screening. It is found that the perturbative solutions of the discrete spectrum can be expressed on the Gamma function, the discreet atomic quantum numbers  and the potential parameters (), in addition to noncommutativity parameters (and). The influence of the induced magnetic field and the coupling parameter of the spin field on some quantum properties of the system have also been studied. The total complete degeneracy of modified energy levels under MCIQP is found to be equal to , which gives a very good indicator that our new treatments produce clear energy values when compared with similar energy levels obtained in ordinary relativistic quantum mechanics (RQM). New mass spectra for the quarkonium systems is found to be equal to the sum of ordinary values in RQM plus two perturbative terms proportional to the parameters (or) and (or) of noncommutativity space-phase. These results are in good agreement with the already existing results in nonrelativistic noncommutative quantum mechanics (NRNCQM) where the physical treatment was done using other potentials such as new modified potential containing Cornell, Gaussian and inverse square terms and modified quark-antiquark interaction potential.