{
  "annotation_id": "d37af66c-bfbf-451f-b42d-344fb2efc340",
  "date_created": "2026-03-02T18:01:59.754000Z",
  "date_modified": "2026-03-02T18:01:59.754000Z",
  "file_hash": "8e41016cfd4a9ce7efeaa495c63005d014dfc9d6def786b4f91946f16c19d8d5",
  "private": false,
  "record": {
    "abstract": "The potentials for a one dimensional Schroedinger equation that are displaced\nalong the x axis under second order Darboux transformations, called 2-SUSY\ninvariant, are characterized in terms of a differential-difference equation.\nThe solutions of the Schroedinger equation with such potentials are given\nanalytically for any value of the energy. The method is illustrated by a\ntwo-soliton potential. It is proven that a particular case of the periodic\nLame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the\ncorresponding Schroedinger equation equation are found for any value of the\nenergy. A simple analytic expression for a family of two-gap potentials is\nderived.",
    "arxiv_id": "quant-ph/0307146",
    "authors": [
      "B F Samsonov",
      "M L Glasser",
      "J Negro",
      "L M Nieto"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/39/306",
    "journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 10053--10069",
    "title": "Second Order Darboux Displacements",
    "url": "https://arxiv.org/abs/quant-ph/0307146"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ddff9db1-eadd-4a61-860e-8017dd6d553d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}