THE INFLUENCE OF DEFORMATION PHASE-SPACE ON SPECTRA OF HEAVY QUARKONIA IN IMPROVED ENERGY POTENTIAL AT FINITE TEMPERATURE MODEL OF SHRODINGER EQUATION VIA THE GENERALIZED BOPP?S SHIFT METHOD AND STANDARD PERTURBATION THEORY

In this work, we obtain solutions of the deformed Schrodinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp's shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium c (c) over bar and bottomonium b (b) over bar at finite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the Q (Q) over bar (Q = c, b) state, the parameters of internal energy potential (T, alpha(s)(T), m(D)(T), beta, c), which are the Debye screening mass m(D)(T), the running coupling constant alpha(s)(T), the critical temperature beta, the free parameter c in addition to noncommutativity parameters (Theta, (theta) over bar). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermiterm. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (c (c) over bar and b (b) over bar). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n(2) in 3D-NRNCPS symmetries instead of the value n(2) in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.