{
  "annotation_id": "61e01f0d-2659-4fa4-8607-80831f02dd3f",
  "date_created": "2026-03-02T18:01:42.003000Z",
  "date_modified": "2026-03-02T18:01:42.003000Z",
  "file_hash": "e35491a840203de424c07dddd4d389fdf0a07dac832560ce8646cd68d1ff781b",
  "private": false,
  "record": {
    "abstract": "It is shown that the energy levels of the one-dimensional nonlinear\nSchrodinger, or Gross-Pitaevskii, equation with the homogeneous trap potential\n$x^{2p}$, $p\\geq 1$, obey an approximate scaling law and as a consequence the\nenergy increases approximately linearly with the quantum number. Moreover, for\na quadratic trap, $p=1$, the rate of increase of energy with the quantum number\nis independent of the nonlinearity: this prediction is confirmed with numerical\ncalculations. It is also shown that the energy levels computed using a\nvariational approximation do not satisfy this scaling law.",
    "arxiv_id": "quant-ph/0012068",
    "authors": [
      "R. Hasson",
      "D. Richards"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1088/0953-4075/34/9/315",
    "title": "A Scaling Law for the Energy Levels of a Nonlinear Schrodinger Equation",
    "url": "https://arxiv.org/abs/quant-ph/0012068"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a2c7da8d-4a75-486e-9f99-e7d813df0278",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}