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

B. Kónya, G. Lévai, Z. Papp

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 a 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.

Original languageEnglish
Pages (from-to)343021-343027
Number of pages7
JournalPhysical Review C - Nuclear Physics
Volume61
Issue number3
Publication statusPublished - Mar 2000

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operators
space bases
scattering
nuclear potential
Hilbert space
integral equations
matrices
approximation
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics

Cite this

Continued fraction representation of the coulomb green's operator and unified description of bound, resonant and scattering states. / Kónya, B.; Lévai, G.; Papp, Z.

In: Physical Review C - Nuclear Physics, Vol. 61, No. 3, 03.2000, p. 343021-343027.

Research output: Contribution to journalArticle

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