{
  "annotation_id": "f419c7eb-5707-451a-9859-944729cc4325",
  "date_created": "2026-03-02T18:02:37.437000Z",
  "date_modified": "2026-03-02T18:02:37.437000Z",
  "file_hash": "132c390e8f21dc811f120f05114d0118ad5a1ce7def2ff6497746e4635542af2",
  "private": false,
  "record": {
    "abstract": "In this paper we use the Lie algebra of space-time symmetries to construct\nstates which are solutions to the time-dependent Schr\\\"odinger equation for\nsystems with potentials $V(x,\\tau)=g^{(2)}(\\tau)x^2+g^{(1)}(\\tau)x\n+g^{(0)}(\\tau)$. We describe a set of number-operator eigenstates states,\n$\\{\\Psi_n(x,\\tau)\\}$, that form a complete set of states but which, however,\nare usually not energy eigenstates. From the extremal state,\n  $\\Psi_0$, and a displacement squeeze operator derived using the Lie\nsymmetries, we construct squeezed states and compute expectation values for\nposition and momentum as a function of time, $\\tau$. We prove a general\nexpression for the uncertainty relation for position and momentum in terms of\nthe squeezing parameters. Specific examples, all corresponding to choices of\n$V(x,\\tau)$ and having isomorphic Lie algebras, will be dealt with in the\nfollowing paper (II).",
    "arxiv_id": "quant-ph/9608008",
    "authors": [
      "Michael Martin Nieto",
      "D. Rodney Truax"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.531836",
    "journal_ref": "J.Math.Phys. 38 (1997) 84-97",
    "title": "Displacement-Operator Squeezed States. I. Time-Dependent Systems Having   Isomorphic Symmetry Algebras",
    "url": "https://arxiv.org/abs/quant-ph/9608008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cbc465b0-5caa-4464-8858-455e6bb3d61d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}