{
  "annotation_id": "1a3f4d3b-7b6c-463a-b717-57539769dd44",
  "date_created": "2026-03-02T18:02:10.013000Z",
  "date_modified": "2026-03-02T18:02:10.013000Z",
  "file_hash": "d18a34e9a3a64002b115837f268ba6410d36f8a2c09f786f6207664c1c2576ef",
  "private": false,
  "record": {
    "abstract": "We have applied the variational $R$-matrix method to calculate the reflection\nand tunneling probabilities of particles tunneling through one-dimensional\npotential barriers for five different types of potential profiles -- truncated\nlinear step, truncated exponential step, truncated parabolic, bell-shaped, and\nEckart. Our variational results for the transmission and reflection\ncoefficients are compared with exact analytical results and results obtained\nfrom other numerical methods. We find that our results are in good agreement\nwith them. We conclude that the variational $R$-matrix method is a simple,\nnon-iterative, and effective method to solve one-dimensional quantum tunneling\nproblems.",
    "arxiv_id": "quant-ph/0407249",
    "authors": [
      "Joseph Kimeu",
      "Roland Mai",
      "Kingshuk Majumdar"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.other",
      "physics.atom-ph"
    ],
    "title": "Application of the variational $R$-matrix method to one-dimensional   quantum tunneling",
    "url": "https://arxiv.org/abs/quant-ph/0407249"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "76ca45e9-a3a3-4018-8e51-006db363661e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}