Algebraic approach to energy spectra of the Scarf type and generalized Pöschl–Teller potentials

Abstract

Using the shape invariance approach, we obtain analytical energy spectra of the Scarf-type and generalized Poschl–Teller potentials and calculate them numerically. The eigenfunctions are also presented for completeness. We find that their eigenfunctions can be expressed by the Nomanovski polynomials and hypergeometric functions, respectively. The key point is how to find their superpotentials using the Sturm–Liouville theorem.