Scattering and bound states for a class of non-central potentials

We obtain L²-series solutions of the three-dimensional Schrödinger wave equation for a large class of non-central potentials that includes, as special cases, the Aharonov-Bohm, Hartmann and magnetic monopole potentials. It also includes contributions of the potential term, cosθ/r² (in spherical coordinates). The solutions obtained are for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The L² bases of the solution space are chosen such that the matrix representation of the wave operator is tridiagonal. The expansion coefficients of the radial and angular components of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations resulting from the matrix wave equation.