Bound State Solution of Radial Schrodinger Equation for the Quark–Antiquark Interaction Potential

This work analytically solved the radial Schrödinger equation with an exponential, generalised, anharmonic Cornell potential using the series expansion method. It also obtained the bound state energy spectra. Through suitable adjustments to the potential parameters, the well-known potential models, such as the pseudoharmonic and Kratzer potentials, were deduced. With the potential parameters also adjusted, the energy spectra for the pseudoharmonic and Kratzer potentials were obtained as special cases. The numerical values of the energy spectra for CO, NO, CH and N2 diatomic molecules were computed for different quantum numbers, n and l, respectively. In addition, with the application of the spectra, an expression for the mass spectra of heavy quarkonium systems (charmonium and bottomonium) was obtained. The results agree with the experimental and theoretical studies in previous works.