dorsal/arxiv
View SchemaContinued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
| Authors | B. Kónya, G. Lévai, Z. Papp |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9908018 |
| URL | https://arxiv.org/abs/nucl-th/9908018 |
| DOI | 10.1103/PhysRevC.61.034302 |
| Journal | Phys.Rev. C61 (2000) 034302 |
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 $\alpha$ particles.
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"abstract": "If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal\n(Jacobi) matrix form in some discrete Hilbert-space basis representation, then\nits Green\u0027s operator can be constructed in terms of a continued fraction. As an\nillustrative example we discuss the Coulomb Green\u0027s operator in\nCoulomb-Sturmian basis representation. Based on this representation, a quantum\nmechanical approximation method for solving Lippmann-Schwinger integral\nequations can be established, which is equally applicable for bound-, resonant-\nand scattering-state problems with free and Coulombic asymptotics as well. The\nperformance of this technique is illustrated with a detailed investigation of a\nnuclear potential describing the interaction of two $\\alpha$ particles.",
"arxiv_id": "nucl-th/9908018",
"authors": [
"B. K\u00f3nya",
"G. L\u00e9vai",
"Z. Papp"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.61.034302",
"journal_ref": "Phys.Rev. C61 (2000) 034302",
"title": "Continued fraction representation of the Coulomb Green\u0027s operator and unified description of bound, resonant and scattering states",
"url": "https://arxiv.org/abs/nucl-th/9908018"
},
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