{
  "annotation_id": "9d9a3232-5e2f-4271-9800-6c714bf19198",
  "date_created": "2026-03-02T18:02:20.532000Z",
  "date_modified": "2026-03-02T18:02:20.532000Z",
  "file_hash": "12e1fe1b02e03a55d212a990a94df359ddfd96226fb9bd6eb0966939d3749cee",
  "private": false,
  "record": {
    "abstract": "Given a non-hermitean matrix M, the structure of its minimal polynomial\nencodes whether M is diagonalizable or not. This note will explain how to\ndetermine the minimal polynomial of a matrix without going through its\ncharacteristic polynomial. The approach is applied to a quantum mechanical\nparticle moving in a square well under the influence of a piece-wise constant\nPT-symmetric potential. Upon discretizing the configuration space, the system\nis decribed by a matrix of dimension three. It turns out not to be\ndiagonalizable for a critical strength of the interaction, also indicated by\nthe transition of two real into a pair of complex energy eigenvalues. The\nsystems develops a three-fold degenerate eigenvalue, and two of the three\neigenfunctions disappear at this exceptional point, giving a difference between\nthe algebraic and geometric multiplicity of the eigenvalue equal to two.",
    "arxiv_id": "quant-ph/0507202",
    "authors": [
      "Stefan Weigert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10582-005-0126-7",
    "journal_ref": "Czech J. Phys. 55 (2005) 1183",
    "title": "How to Test for Diagonalizability: The Discretized PT-Invariant   Square-Well Potential",
    "url": "https://arxiv.org/abs/quant-ph/0507202"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8e0bba53-70bf-4109-bc64-b61fe0b1cdd9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}