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

Abstract

We obtain an analytic approximation of the bound states solution of the Schrödinger equation on the 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 the class of exactly solvable problems. The solutions are finite series (with a small number of terms) of square integrable functions written in terms of Romanovski–Jacobi polynomials.

Keywords

• tridiagonal representation
• orthogonal polynomials
• recursion relation
• energy spectrum
• Romanovski–Jacobi polynomials