| Quantum mechanical Hamilton operators, in some discrete Hilbert-space basis representation, often have infinite symmetric band-matrix structures. In this work, a computational method is developed to determine the corresponding Green's operators. The knowledge of the Green's operator is equivalent to the complete solution of the quantum mechanical problem. If the Hamiltonian is tridiagonal, like in the case of the D-dimensional Coulomb and harmonic oscillator problem, the Green's operator is constructed in terms of continued fractions, which can be connected to the 2F1 hypergeometric functions. If the Hamiltonian has a band-matrix structure, like in the case of Coulomb or harmonic oscillator with polynomial perturbations, the Green's operator is constructed in terms of matrix-valued continued fraction. |
