{
  "annotation_id": "ed8deeea-d37a-4c21-826a-e713b77963d6",
  "date_created": "2026-03-02T18:01:38.354000Z",
  "date_modified": "2026-03-02T18:01:38.354000Z",
  "file_hash": "eec2f1a419b2be58d73b352f14526771e0bd63cd4e2cc6e306ce983a304ed439",
  "private": false,
  "record": {
    "abstract": "We derive an exact analytic solution to a Klein-Gordon equation for a step\npotential barrier with cutoff plane wave initial conditions, in order to\nexplore wave evolution in a classical forbidden region. We find that the\nrelativistic solution rapidly evanesces within a depth $2x_p$ inside the\npotential, where $x_p$ is the penetration length of the stationary solution.\nBeyond the characteristic distance $2x_p$, a Sommerfeld-type precursor travels\nalong the potential at the speed of light, $c$. However, no spatial propagation\nof a main wavefront along the structure is observed. We also find a non-causal\ntime evolution of the wavefront peak. The effect is only an apparent violation\nof Einstein causality.",
    "arxiv_id": "quant-ph/0008084",
    "authors": [
      "Jorge Villavicencio"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/33/34/311",
    "title": "Exact relativistic time evolution for a step potential barrier",
    "url": "https://arxiv.org/abs/quant-ph/0008084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dfae84a3-63cf-4c8a-9495-73c01b5d49fc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}