dorsal/arxiv
View SchemaMany-body system with a four-parameter family of point interactions in one dimension
| Authors | F A B Coutinho, Y Nogami, Lauro Tomio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903098 |
| URL | https://arxiv.org/abs/quant-ph/9903098 |
| DOI | 10.1088/0305-4470/32/26/311 |
| Journal | J.Phys.A32:4931-4942,1999 |
Abstract
We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $\delta$-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the $\delta$-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is not satisfied except when the four-parameter family is essentially reduced to the $\delta$-function potential.
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"abstract": "We consider a four-parameter family of point interactions in one dimension.\nThis family is a generalization of the usual $\\delta$-function potential. We\nexamine a system consisting of many particles of equal masses that are\ninteracting pairwise through such a generalized point interaction. We follow\nMcGuire who obtained exact solutions for the system when the interaction is the\n$\\delta$-function potential. We find exact bound states with the four-parameter\nfamily. For the scattering problem, however, we have not been so successful.\nThis is because, as we point out, the condition of no diffraction that is\ncrucial in McGuire\u0027s method is not satisfied except when the four-parameter\nfamily is essentially reduced to the $\\delta$-function potential.",
"arxiv_id": "quant-ph/9903098",
"authors": [
"F A B Coutinho",
"Y Nogami",
"Lauro Tomio"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/32/26/311",
"journal_ref": "J.Phys.A32:4931-4942,1999",
"title": "Many-body system with a four-parameter family of point interactions in one dimension",
"url": "https://arxiv.org/abs/quant-ph/9903098"
},
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