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Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

B. Kónya·G. Lévai·Z. Papp
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Abstract

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $α$ particles.

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B. Kónya, G. Lévai, Z. Papp. 1999-10-27. Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states. https://doi.org/10.1103/physrevc.61.034302

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