{
  "annotation_id": "a84d0939-f5dc-4b84-a5b9-2b4354d6908f",
  "date_created": "2026-03-02T18:02:48.527000Z",
  "date_modified": "2026-03-02T18:02:48.527000Z",
  "file_hash": "05d7d4c631fe5b2d14b793a424780d307cf7994b1401e98322a5bcffdfe23335",
  "private": false,
  "record": {
    "abstract": "Darboux transformation operators that produce multisoliton potentials are\nanalyzed as operators acting in a Hilbert space. Isometric correspondence\nbetween Hilbert spaces of states of a free particle and a particle moving in a\nsoliton potential is established. It is shown that the Darboux transformation\noperator is unbounded but closed and can not realize an isometric mapping\nbetween Hilbert spaces. A quasispectral representation of such an operator in\nterms of continuum bases is obtained. Different types of coherent states of a\nmultisoliton potential are introduced. Measures that realize the resolution of\nthe identity operator in terms of the projectors on the coherent states vectors\nare calculated. It is shown that when these states are related with free\nparticle coherent states by a bounded symmetry operator the measure is defined\nby ordinary functions and in the case of a semibounded symmetry operator the\nmeasure is defined by a generalized function.",
    "arxiv_id": "quant-ph/9904090",
    "authors": [
      "Boris F. Samsonov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/33/3/312",
    "journal_ref": "J.Phys.A33:591-605,2000",
    "title": "Coherent States for Transparent Potentials",
    "url": "https://arxiv.org/abs/quant-ph/9904090"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0449319a-fb9a-4d0f-a22e-13796f9fec22",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}