{
  "annotation_id": "ad11d04d-bbb2-402c-9742-916f6bf81c53",
  "date_created": "2026-03-02T18:02:06.982000Z",
  "date_modified": "2026-03-02T18:02:06.982000Z",
  "file_hash": "9a52750f9dc518ea6cccd6d5a6a04e37a7b00727288533405ff0b0e1a121b323",
  "private": false,
  "record": {
    "abstract": "Analytical solutions to the time-dependent Shr\\\"{o}dinger equation in one\ndimension are developed for time-independent potentials, one consisting of an\ninfinite wall and a repulsive delta function. An exact solution is obtained by\nmeans of a convolution of time-independent solutions spanning the given Hilbert\nspace with appropriately chosen spectral functions. Square-integrability and\nthe boundary conditions are satisfied. The probability for the particle to be\nfound inside the potential well is calculated and shown to exhibit\nnon-exponential decay decreasing at large times as $t^{-3}$. The result is\ngeneralized for all square-integrable solutions to this problem.",
    "arxiv_id": "quant-ph/0403177",
    "authors": [
      "Athanasios N. Petridis",
      "Lawrence P. Staunton",
      "Jon Vermedahl",
      "Marshall Luban"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An Exact Solution to the Time-dependent Schrodinger Equation for a Model   One-dimensional Potential",
    "url": "https://arxiv.org/abs/quant-ph/0403177"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "217a4c07-26c0-4a01-92a5-e3facc9e28ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}