{
  "annotation_id": "5b670cfa-0823-414b-85c2-894dd287a572",
  "date_created": "2026-03-02T18:02:10.390000Z",
  "date_modified": "2026-03-02T18:02:10.390000Z",
  "file_hash": "f655ea9f8c96c4bb2baa2ba43148c944ab1f12c71b26a603d18438df80e8e972",
  "private": false,
  "record": {
    "abstract": "The autocorrelation function, A(t), measures the overlap (in Hilbert space)\nof a time-dependent quantum mechanical wave function, psi(x,t), with its\ninitial value, psi(x,0). It finds extensive use in the theoretical analysis and\nexperimental measurement of such phenomena as quantum wave packet revivals. We\nevaluate explicit expressions for the autocorrelation function for\ntime-dependent Gaussian solutions of the Schrodinger equation corresponding to\nthe cases of a free particle, a particle undergoing uniform acceleration, a\nparticle in a harmonic oscillator potential, and a system corresponding to an\nunstable equilibrium (the so-called `inverted\u0027 oscillator.) We emphasize the\nimportance of momentum-space methods where such calculations are often more\nstraightforwardly realized, as well as stressing their role in providing\ncomplementary information to results obtained using position-space\nwavefunctions.",
    "arxiv_id": "quant-ph/0408050",
    "authors": [
      "R. W. Robinett",
      "L. C. Bassett"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10702-004-1119-7",
    "title": "Analytic results for Gaussian wave packets in four model systems: II.   Autocorrelation functions",
    "url": "https://arxiv.org/abs/quant-ph/0408050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7bb95ffb-70e6-4582-beb5-982d6ab614c0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}