Polynomial solutions of the radial Schrodinger equation

In this paper, we investigate the possibility of finding polynomial solutions to central potentials of the radial Schrödinger equation. By setting up the proper conditions that join the potential's parameters to each other as well as eventual wave function's zeros, exactly solvable potentials under these conditions have been achieved and expressions for energy levels are formed. Further, we find a good agreement between our results and that published in the literature. Results found here could be very useful in generating realistic tools to solve further complicated physical systems. (paper)