Analytical approximation to the ℓ-wave solutions of the Eckart potential in the tridiagonal representation

Abstract

By working in a completely square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator, the arbitrary ℓ-wave solutions of the Schrödinger equation for the Eckart potential are investigated with an approximation scheme of the centrifugal term. The three-term recursion relation for the expansion coefficients of the wavefunction is presented. The bound state wavefunctions are expressed in terms of the Jacobi polynomial, and the discrete spectrum for the bound states is obtained by diagonalization of the recursion relation.