{
  "annotation_id": "377d6fb1-8b9b-499d-834d-e80356dcb23f",
  "date_created": "2026-03-02T18:02:29.887000Z",
  "date_modified": "2026-03-02T18:02:29.887000Z",
  "file_hash": "8ed664311abed59772a6fb6a061299b22f2268dc67a4eba1242f9b1751416e8b",
  "private": false,
  "record": {
    "abstract": "The one dimensional Schroedinger hydrogen atom is an interesting mathematical\nand physical problem to study bound states, eigenfunctions and quantum\ndegeneracy issues. This 1D physical system gave rise to some intriguing\ncontroversy over more than four decades. Presently, still no definite consensus\nseems to have been reached. We reanalyzed this apparently controversial\nproblem, approaching it from a Fourier transform representation method combined\nwith some fundamental (basic) ideas found in self-adjoint extensions of\nsymmetric operators. In disagreement with some previous claims, we found that\nthe complete Balmer energy spectrum is obtained together with an odd parity set\nof eigenfunctions. Closed form solutions in both coordinate and momentum spaces\nwere obtained. No twofold degeneracy was observed as predicted by the\ndegeneracy theorem in one dimension, though it does not necessarily have to\nhold for potentials with singularities. No ground state with infinite energy\nexists since the corresponding eigenfunction does not satisfy the Schroedinger\nequation at the origin.",
    "arxiv_id": "quant-ph/0608038",
    "authors": [
      "G. Palma",
      "U. Raff"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1139/P06-072",
    "title": "The one dimensional Hydrogen atom revisited",
    "url": "https://arxiv.org/abs/quant-ph/0608038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4ce87dac-6aaf-4153-b359-95d902ed2652",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}