{
  "annotation_id": "cfe5d3e5-1c7c-4c48-aa21-052e3fc4f226",
  "date_created": "2026-03-02T18:01:46.119000Z",
  "date_modified": "2026-03-02T18:01:46.119000Z",
  "file_hash": "b87e04b7cc6de309abf02e2f22c4951d49ec2371a7412b6e46b30c84b70ae59c",
  "private": false,
  "record": {
    "abstract": "The method of intertwining with n-dimensional (nD) linear intertwining\noperator L is used to construct nD isospectral, stationary potentials. It has\nbeen proven that differential part of L is a series in Euclidean algebra\ngenerators. Integrability conditions of the consistency equations are\ninvestigated and the general form of a class of potentials respecting all these\nconditions have been specified for each n=2,3,4,5. The most general forms of 2D\nand 3D isospectral potentials are considered in detail and construction of\ntheir hierarchies is exhibited. The followed approach provides coordinate\nsystems which make it possible to perform separation of variables and to apply\nthe known methods of supersymmetric quantum mechanics for 1D systems. It has\nbeen shown that in choice of coordinates and L there are a number of\nalternatives increasing with $n$ that enlarge the set of available potentials.\nSome salient features of higher dimensional extension as well as some\napplications of the results are presented.",
    "arxiv_id": "quant-ph/0111034",
    "authors": [
      "S. Kuru",
      "A. Tegmen",
      "A. Vercin"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "nlin.SI"
    ],
    "doi": "10.1063/1.1383787",
    "journal_ref": "J. Math. Phys. 42 (2001) 3344-3360",
    "title": "Intertwined isospectral potentials in an arbitrary dimension",
    "url": "https://arxiv.org/abs/quant-ph/0111034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15365201-935b-4ae8-932c-140086093423",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}