{
  "annotation_id": "7bdee5e1-91f6-4fc0-9a42-1ee90e506078",
  "date_created": "2026-03-02T18:01:52.632000Z",
  "date_modified": "2026-03-02T18:01:52.632000Z",
  "file_hash": "e4aadc2a61e3c71ac0b165113212902f61a2a860a6c98aec8fe595aae19609ea",
  "private": false,
  "record": {
    "abstract": "By using an exact solution to the time-dependent Schr\\\"{o}dinger equation\nwith a point source initial condition, we investigate both the time and spatial\ndependence of quantum waves in a step potential barrier. We find that for a\nsource with energy below the barrier height, and for distances larger than the\npenetration length, the probability density exhibits a {\\it forerunner}\nassociated with a non-tunneling process, which propagates in space at exactly\nthe semiclassical group velocity. We show that the time of arrival of the\nmaximum of the {\\it forerunner} at a given fixed position inside the potential\nis exactly the traversal time, $\\tau$. We also show that the spatial evolution\nof this transient pulse exhibits an invariant behavior under a rescaling\nprocess. This analytic property is used to characterize the evolution of the\n{\\it forerunner}, and to analyze the role played by the time of arrival,\n$3^{-1/2}\\tau$, found recently by Muga and B\\\"{u}ttiker [Phys. Rev. A {\\bf 62},\n023808 (2000)].",
    "arxiv_id": "quant-ph/0210010",
    "authors": [
      "Jorge Villavicencio",
      "Roberto Romo",
      "Sukey Sosa y Silva"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.042110",
    "title": "Quantum-wave evolution in a step potential barrier",
    "url": "https://arxiv.org/abs/quant-ph/0210010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "916c0d0f-db8c-4587-8ba8-7eab4517ab65",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}