Analytical arbitrary ?-wave solutions of the manning-rosen potential in the tridiagonalization program

摘要

By working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator, the arbitrary ?-wave solutions of the Schr?dinger equation for the Manning-Rosen potential is investigated with an approximation of centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented. The bound-state wavefunctions are expressed in terms of the Jocobi polynomial, and the discrete spectrum of the bound states is obtained by diagonalization of the recursion relation.