A new conjecture for obtaining the energy spectra of the wave equations under solvable potentials

In this paper, we proposed a new method for obtaining the energy of a particle which can be described by the wave equations under a solvable potential function. The method is constructed using the Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Furthermore, the method is conjectured using the approximation of the orthogonal polynomial embedded in the eigenfunctions of Nikiforov–Uvarov approach. The approximated wave function is exact with the wave function derived from supersymmetry. After some algebraic approach, the energy can be obtained in closed form. The method is simple and does not require solving complex integrals and laborious processes that are associated with some methods in the existing literature.