Solutions of the Schrödinger equation in the tridiagonal representation with the deformed hyperbolic potentials

Abstract

The Schrödinger equation for the one-dimensional ‘deformed’ Rosen–Morse potential and the ‘deformed’ hyperbolic single-wave potential is investigated by using the tridiagonal program. In this program, solving the wave equation is mapping into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunctions. The wavefunctions are written in terms of orthogonal polynomials, some of which are modified versions of the known polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation.