Analytical Solutions of the Manning-Rosen Potential In the Tridiagonal Program

The Schrödinger equation with the Manning-Rosen potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. In this program, solving the Schrödinger equation is translated into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation with special choice of the parameters and the wavefunctions is expressed in terms of the Jocobi polynomial.