dorsal/arxiv
View SchemaMulti-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
| Authors | M. Braun, S. A. Sofianos, H. Leeb |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301154 |
| URL | https://arxiv.org/abs/quant-ph/0301154 |
| DOI | 10.1103/PhysRevA.68.012719 |
Abstract
We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.
{
"annotation_id": "63353f43-253a-41ec-9fd9-2edea28e71bc",
"date_created": "2026-03-02T18:01:56.379000Z",
"date_modified": "2026-03-02T18:01:56.379000Z",
"file_hash": "7aa394d6749d7dee038841f20ca0e0385685e4d925ef3c62868d145058adf9c7",
"private": false,
"record": {
"abstract": "We consider the multi-channel inverse scattering problem in one-dimension in\nthe presence of thresholds and bound states for a potential of finite support.\nUtilizing the Levin representation, we derive the general Marchenko integral\nequation for N-coupled channels and show that, unlike to the case of the radial\ninverse scattering problem, the information on the bound state energies and\nasymptotic normalization constants can be inferred from the reflection\ncoefficient matrix alone. Thus, given this matrix, the Marchenko inverse\nscattering procedure can provide us with a unique multi-channel potential. The\nrelationship to supersymmetric partner potentials as well as possible\napplications are discussed. The integral equation has been implemented\nnumerically and applied to several schematic examples showing the\ncharacteristic features of multi-channel systems. A possible application of the\nformalism to technological problems is briefly discussed.",
"arxiv_id": "quant-ph/0301154",
"authors": [
"M. Braun",
"S. A. Sofianos",
"H. Leeb"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.012719",
"title": "Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States",
"url": "https://arxiv.org/abs/quant-ph/0301154"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "85c0579f-21c3-4c77-9b9a-9c62611e02cb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}