New bound state solutions of diatomic molecules and mass spectrum of heavy quarkonium with improved modified Kratzer potential plus screened Coulomb potential model in the framework of three-dimensional nonrelativistic noncommutative phase-space symmetries

Approximate analytical solutions of the modified Schrodinger equation have been obtained with a combination of two proposed potentials, called the improved modified Kratzer potential plus screened Coulomb (IMKSC) potential, using the approximation scheme to the centrifugal term for any l-states. We applied the generalized Bopp's shift method and standard perturbation theory. IMKSC is a superposition of modified Kratzer potential plus screened Coulomb (MKSC) potential, and new terms appear as a result of the effects of the noncommutativity properties of space and phase potential on the MKSC potential. The new bound state energy eigenvalues for some diatomic molecules were obtained in terms of the discrete atomic quantum numbers (j,n,s,m), the infinitesimal NC phase-space parameters, the dissociation energy, the equilibrium internuclear separation, the depth of the potential, and the range of the potential. Furthermore, we have shown that the NC-Hamiltonian operator is the sum of the Hamiltonian operator of the MKSC potential, the perturbed spin-orbit, and the modified Zeeman operator. The new mass spectra of heavy quarkonium systems are calculated using the new energy spectrum expression. It appears as a combination of corresponding values in the literature plus an infinitesimal part that describes the deformation phase-space.