L2 Discretization of the Coulomb Three-body Problem in A Non-orthogonal Laguerre-function Basis - Agus Kartono (Jurnal Matematika & Sains, 2006)
In this paper a general analysis of the three-body Coulomb potential polynomials was presented. The three-body Coulomb wave functions expansion in a non-orthogonal Laguerre-type base function is shown to give two modified Pollaczek polynomials. The frozen-core model is used to examine the three-body Coulomb Hamiltonian. The resulting three-term recurrence relation is a special case of the Pollaczek polynomials which is a set of orthogonal polynomials having a nonempty continuous spectrum in addition to an infinite discrete spectrum. The completeness of the three-body Coulomb wave functions is further studied for different Laguerre basis size.