{
  "annotation_id": "9f2596e1-247f-40de-adc6-3823c968f1e5",
  "date_created": "2026-03-02T18:02:34.316000Z",
  "date_modified": "2026-03-02T18:02:34.316000Z",
  "file_hash": "328d9229324e510717a352fae47b99dde57f43bcd4cd1663fd5df2c4b6e24ced",
  "private": false,
  "record": {
    "abstract": "In the present work the conditions appearing in the WKB approximation\nformalism of quantum mechanics are analyzed. It is shown that, in general, a\ncareful definition of an approximation method requires the introduction of two\nlength parameters, one of them always considered in the text books on quantum\nmechanics, whereas the second one is usually neglected. Afterwards we define a\nparticular family of potentials and prove, resorting to the aforementioned\nlength parameters, that we may find an energy which is a lower bound to the\nground energy of the system. The idea is applied to the case of a harmonic\noscillator and also to a particle freely falling in a homogeneous gravitational\nfield, and in both cases the consistency of our method is corroborated. This\napproach, together with the Rayleigh--Ritz formalism, allows us to define an\nenergy interval in which the ground energy of any potential, belonging to our\nfamily, must lie.",
    "arxiv_id": "quant-ph/0702213",
    "authors": [
      "Luis F. Barragan-Gil",
      "Abel Camacho"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217732307022979",
    "title": "WKB formalism and a lower limit for the energy eigenstates of bound   states for some potentials",
    "url": "https://arxiv.org/abs/quant-ph/0702213"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f43767e5-ab7a-4fe5-a35e-e9eae68bd9b6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}