A New Nonrelativistic Investigation for Spectra of Heavy Quarkonia with Modified Cornell Potential: Noncommutative Three Dimensional Space and Phase Space Solutions

Abstract

In this paper, we present a further investigation for the exact solvability of non-relativistic quantum spectrum systems for modified Cornell potential (m.c.p.) by means Boopp’s shift method instead to solving deformed Schrödinger equation (d.s.e.) with star product, in the framework of both noncommutativity three dimensional real space and space phase (NC: 3D-RSP). The exact corrections for lowest excitations states: ground and first excited states are found straightforwardly for interactions for quarkouniom systems (qq with q = c, b,... ) by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on: four infinitesimals parameters, which are induced by position-position and momentum-momentum noncommutativity, the Cornell potential parameters and the discreet atomic quantum numbers: (j, l, s and m) and we have also shown that, the usual states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2 N (2l+1) sub-states in the new quantum symmetries of (NC: 3D-RSP). It is shown that the (d.s.e.) for (m.c.p.) has the similar behaviors to the relativistic Dirac equation which the polarities of fermionic particle appear exciplicitly.