{
  "annotation_id": "5b803aee-c8ad-4a21-b193-a1bbd04a8500",
  "date_created": "2026-03-02T18:02:44.483000Z",
  "date_modified": "2026-03-02T18:02:44.483000Z",
  "file_hash": "98d4002d8d82065e78292bd9148250f070c5679e1efcc8198e3155d69fca0c90",
  "private": false,
  "record": {
    "abstract": "An exact solution of the energy shift in each quantum mechanical energy\nlevels in a one dimensional symmetrical linear harmonic oscillator has been\ninvestigated. The solution we have used here is firstly derived by manipulating\nSchrodinger differential equation to be confluent hypergeometric differential\nequation. The final exact numerical results of the energy shifts are then found\nby calculating the final analytical solution of the confluent hypergeometric\nequation with the use of a software (Mathcad Plus 6.0) or a program programmed\nby using Turbo Pascal 7.0. We find that the results of the energy shift in our\nexact solution method are almost the same as that in Barton et. al.\napproximation method. Thus, the approximation constants (obliquity factors)\nappeared in Barton et. al. method can also be calculated using the results of\nthe exact method.",
    "arxiv_id": "quant-ph/9901009",
    "authors": [
      "Hendry I. Elim"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP",
      "physics.chem-ph"
    ],
    "title": "Exact Solution of the Energy Shift in each Quantum Mechanical Energy   Levels in a One Dimensional Symmetrical Linear Harmonic Oscillator",
    "url": "https://arxiv.org/abs/quant-ph/9901009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "339a8b01-8d4e-4db0-8525-20e33bd5c26a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}