{
  "annotation_id": "602b8d2a-d87b-4305-9b92-4ad33802d657",
  "date_created": "2026-03-02T18:02:41.586000Z",
  "date_modified": "2026-03-02T18:02:41.586000Z",
  "file_hash": "b75f729bc44d259554ec27f1f793b90ed927493165ed09f81178adf939062f54",
  "private": false,
  "record": {
    "abstract": "The spectra and generalized eigenfunctions of the hyperbolic and parabolic\ngenerators of the standard representation of SU(1,1) in the one-mode boson\nHilbert space are derived. The eigenfunctions are given in three different\nforms, corresponding to the coordinate, photon number, and Fock-Bargmann\nrepresentations of the state vectors. The possible spectra of general second\ndegree Hamiltonians are determined. Some corresponding results in the two-mode\ncase are also given. - In the Appendix we prove completeness and orthonormality\nrelations for the polynomials giving the number representation expansion\ncoefficients of the generalized eigenfunctions of the hyperbolic generator (=\nsqueezing generator). These polynomials are special cases of Pollaczek\npolynomials.",
    "arxiv_id": "quant-ph/9711018",
    "authors": [
      "Bengt Nagel"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Spectra and generalized eigenfunctions of the one- and two-mode   squeezing operators in quantum optics",
    "url": "https://arxiv.org/abs/quant-ph/9711018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4355729e-5229-4fa7-9d72-6fb4c9371a60",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}