Tridiagonal treatment for the Schrödinger equation with a noncentral electric dipole ring-shaped potential

Abstract

A noncentral potential is proposed in which the noncentral electric dipole and a ring-shaped component \({\cos ^{2}\theta/r^{2}\sin^{2}\theta}\) are included. The exactly complete solutions of the Schrodinger equation with this potential is investigated by working in a complete square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator. The solutions obtained are for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the wavefunctions (both angular and radial) are written in terms of orthogonal polynomials satisfying three-term recursion relation. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.