The quarkonium spectroscopy has been studied by considering a non-relativistic potential which includes the QCD vacuum polarization corrections. The potential consists of a short-range 2-loop QCD potential matched to a Martin-type power law potential for large distances. The Poggio-Schnitzer correction to the leptonic decay width has also been included. The energy levels, leptonic decay widths and E1 transition rates ofψ and γ families have been calculated and have been found to be in good agreement with experimental results. The toponium spectroscopy has also been studied for the range ofM, values suggested by the recent jet events observed by the UA1 collaboration. The contribution of the decay through a virtualZ⁰ has also been included in the calculation. The potential seems to provide a very good non-relativistic description of the quarkonium systems.