{
  "annotation_id": "35ec5f29-2404-492c-873b-ec24c35c45e9",
  "date_created": "2026-03-02T18:02:24.079000Z",
  "date_modified": "2026-03-02T18:02:24.079000Z",
  "file_hash": "e7bcbbe9c67943825cec2929b1ba0d55c639142943d4fba6262cc1e7f6eaf0d6",
  "private": false,
  "record": {
    "abstract": "We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the\nHamiltonians having a number of Jordan cells in particular biorthogonal bases.\nThe \"self-orthogonality\" phenomenon is clarified in terms of a correct spectral\ndecomposition and it is shown that \"self-orthogonal\" states never jeopardize\nresolution of identity and thereby quantum averages of observables. The example\nof a complex potential leading to one Jordan cell in the Hamiltonian is\nconstructed and its origin from level coalescence is elucidated. Some puzzles\nwith zero-binorm bound states in continuous spectrum are unraveled with the\nhelp of a correct resolution of identity.",
    "arxiv_id": "quant-ph/0602207",
    "authors": [
      "A. V. Sokolov",
      "A. A. Andrianov",
      "F. Cannata"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "hep-th",
      "math-ph",
      "math.MP",
      "physics.atom-ph",
      "physics.chem-ph"
    ],
    "doi": "10.1088/0305-4470/39/32/S20",
    "journal_ref": "J.Phys. A39 (2006) 10207-10228",
    "title": "Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians:   puzzles with self-orthogonal states",
    "url": "https://arxiv.org/abs/quant-ph/0602207"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "019253c9-8edf-476c-b904-45488590d450",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}