A novel approach for heavy quarkonium spectra

In this work, we attempt to investigate heavy quark systems ( and ) in the non-relativistic framework using phenomenological inter-quark potentials. For this reason, we have developed a powerful and flexible theoretical formalism, within the frame of the Schrödinger equation, to use for the analysis of heavy quarkonium systems involving exactly solvable energy-dependent potentials, together with quasi-/conditionally-solvable and non-solvable interaction potentials. Our first application to exactly solvable systems has clarified that energy dependent term in the potential leads to saturation of the spectra and degree of saturation is governed by the magnitude of perturbation. Second application to quasi-exactly solvable potentials, which is the Coulomb plus linear potential with a quadratic term, has justified the success of the present formalism due to its wide range of applicability, considering the comparison of the findings obtained by the present approach with those of experimental results and the other theoretical predictions in the related literature. Finally, the application of this new technique to also non-solvable systems involving Cornell potential has shed some light on the questions concerning with the limitations of the traditional perturbation techniques.