Green's operator for Hamiltonians with Coulomb plus polynomial potentials

The Hamiltonian of a Coulomb plus polynomial potential in the Coulomb–Sturmian basis has an infinite symmetric band-matrix structure. A band matrix can always be considered as a block-tridiagonal matrix. So, the corresponding Green's operator can be given as a matrix-valued continued fraction. As examples, we calculate Green's operator for the Coulomb plus linear and quadratic confinement potential problems and determine the energy levels.