Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation

Abstract

The Schrödinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The arbitrary ℓ-wave solutions are obtained by using an approximation of the centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jacobi polynomial. The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.