Finite-Series Approximation of the Bound States for Two Novel Potentials

We obtain an analytic approximation of the bound states solution Schrödinger equation on semi-infinite real line for two potential models with a rich structure as shown by their spectral phase diagrams. These potentials do not belong to class exactly solvable problems. The solutions are finite series (with small number terms) square integrable functions written in terms Romanovski–Jacobi polynomials.