On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
arXiv:math-ph/0604037 · doi:10.1103/PhysRevA.74.014701
Abstract
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the inverse of the Green's matrix. The continued fraction can be transformed to a ratio of two $_{2}F_{1}$ hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.
8 pages