An approach to heavy quarkonium spectra

An application of the recently introduced method [M. Capak et al., J. Math. Phys. 52, 102102 ( 2011)] to the bound-state eigenvalue problem in the elementary quarkonium potential V(r) = -a/r + br + cr(2) is described, proved and illustrated for c (c) over bar and b (b) over bar systems. The quasi- and conditionally-exactly solvable spin-averaged mass spectra of heavy quarkonia are obtained in compact forms. The comparison of the present predictions with those of other theories in the related literature, together with the available data, has shown the success of the model used in this work and also revealed that the use of different confinings in the perturbed Coulomb potential descriptions has no considerable effect on the mass spectra of such systems.