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

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.

arXiv comment8 pages

References in corpus (7)

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• Three-potential formalism for the three-body Coulomb scattering problem
• Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials
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• Approximations of potentials through the truncation of their inverses
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• Faddeev-Merkuriev integral equations for atomic three-body resonances
• Calculation of Relativistic Single-Particle States
• Series of broad resonances in atomic three-body systems