Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states - art. no. 034302

If a quantum-mechanical Hamiltonian has an infinite symmetric tridiagonal ( Jacobi) matrix form in some discrete Hilbert-space basis representation, th en its Green's operator can be constructed in terms of a continued fraction . As an illustrative example we discuss the Coulomb Green's operator in a C oulomb-Sturmian basis representation. Based on this representation, a quant um-mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, reson ant- and scattering-state problems with free and Coulombic asymptotics as w ell. The performance of this technique is illustrated with a detailed inves tigation of a nuclear potential describing the interaction of two ru partic les.