On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
Mathematical Physics
2009-11-11 v1 math.MP
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 hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.
Keywords
Cite
@article{arxiv.math-ph/0604037,
title = {On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator},
author = {F. Demir and Z. T. Hlousek and Z. Papp},
journal= {arXiv preprint arXiv:math-ph/0604037},
year = {2009}
}
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8 pages