The Orthogonal Polynomial Projection Quantization Method and Exactly Solvable Quantum Systems: A Moment Representation Shortcut to the Nikiforov-Uvarov Approach

We show how two formulations of the Orthogonal Polynomial Projection Quantization Method (OPPQ) recently developed by Handy and Vrinceanu (J. Phys. A: Math. {\&} Theor.: \textbf{46}, 135202 (2013); J. Phys. B: At. Mol. Opt. Phys. \textbf{46}, 115002 (2013)) yield exact energies for one dimensional Exactly Solvable Quantum Systems. The second of these yields explicit closed form expressions for the discrete state energies. Our formulation bypasses the intricacies of the Nikiforov-Uvarov approach, popular among many researchers. We review most of these problems outlining their analysis through the two formulations of OPPQ.