On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator

Details On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator

2006-04-17

arxiv.org/abs/math-ph/0604037v1

Physics

Mathematical Physics

8 pages

Scientific paper

10.1103/PhysRevA.74.014701

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.

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