### 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 language | English |
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Pages (from-to) | 343021-343027 |

Number of pages | 7 |

Journal | Physical Review C - Nuclear Physics |

Volume | 61 |

Issue number | 3 |

Publication status | Published - Mar 2000 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review C - Nuclear Physics*,

*61*(3), 343021-343027.

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

Research output: Contribution to journal › Article

*Physical Review C - Nuclear Physics*, vol. 61, no. 3, pp. 343021-343027.

}

TY - JOUR

T1 - Continued fraction representation of the coulomb green's operator and unified description of bound, resonant and scattering states

AU - Kónya, B.

AU - Lévai, G.

AU - Papp, Z.

PY - 2000/3

Y1 - 2000/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17144441856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17144441856&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:17144441856

VL - 61

SP - 343021

EP - 343027

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 3

ER -