dorsal/arxiv
View SchemaRealization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths
| Authors | T. Shigehara, H. Mizoguchi, T. Mishima, Taksu Cheon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812006 |
| URL | https://arxiv.org/abs/quant-ph/9812006 |
| Journal | IEICE Trans.Fund.Elec.Comm.Comp.Sci. E82-A (1999) 1708-1713 |
Abstract
We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil C^{\infty}_{0}({\bf R} \backslash\{0\})$. It is achieved in the small distance limit of equally spaced three neighboring Dirac's $\delta$ potentials. The strength for each $\delta$ is appropriately renormalized according to the distance and it diverges, in general, in the small distance limit. The validity of our method is ensured by numerical calculations. In general cases except for usual $\delta$, the wave function discontinuity appears around the interaction and one can observe such a tendency even at a finite distance level.
{
"annotation_id": "21d5a9e5-5e28-4da2-b5b0-c47825e6f0ac",
"date_created": "2026-03-02T18:02:45.236000Z",
"date_modified": "2026-03-02T18:02:45.236000Z",
"file_hash": "87474115a965165d2b6a161b5140b86631af236bc11058efb43b601e9861590f",
"private": false,
"record": {
"abstract": "We propose a new method to construct a four parameter family of\nquantum-mechanical point interactions in one dimension, which is known as all\npossible self-adjoint extensions of the symmetric operator $T=-\\Delta \\lceil\nC^{\\infty}_{0}({\\bf R} \\backslash\\{0\\})$. It is achieved in the small distance\nlimit of equally spaced three neighboring Dirac\u0027s $\\delta$ potentials. The\nstrength for each $\\delta$ is appropriately renormalized according to the\ndistance and it diverges, in general, in the small distance limit. The validity\nof our method is ensured by numerical calculations. In general cases except for\nusual $\\delta$, the wave function discontinuity appears around the interaction\nand one can observe such a tendency even at a finite distance level.",
"arxiv_id": "quant-ph/9812006",
"authors": [
"T. Shigehara",
"H. Mizoguchi",
"T. Mishima",
"Taksu Cheon"
],
"categories": [
"quant-ph",
"cond-mat",
"nucl-th"
],
"journal_ref": "IEICE Trans.Fund.Elec.Comm.Comp.Sci. E82-A (1999) 1708-1713",
"title": "Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths",
"url": "https://arxiv.org/abs/quant-ph/9812006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c8dbffb3-6946-4418-91c6-b996dbf9e7fa",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}