{
  "annotation_id": "d476b126-420b-47d1-9ecd-551aeb012647",
  "date_created": "2026-03-02T18:02:12.977000Z",
  "date_modified": "2026-03-02T18:02:12.977000Z",
  "file_hash": "d8bba06dbbfb509ebb2280645993c6e5e3916301ff47fafa8e2b2845cfecd808",
  "private": false,
  "record": {
    "abstract": "For a wide class of Hamiltonians, a novel method to obtain lower and upper\nbounds for the lowest energy is presented. Unlike perturbative or variational\ntechniques, this method does not involve the computation of any integral (a\nnormalisation factor or a matrix element). It just requires the determination\nof the absolute minimum and maximum in the whole configuration space of the\nlocal energy associated with a normalisable trial function (the calculation of\nthe norm is not needed). After a general introduction, the method is applied to\nthree non-integrable systems: the asymmetric annular billiard, the many-body\nspinless Coulombian problem, the hydrogen atom in a constant and uniform\nmagnetic field. Being more sensitive than the variational methods to any local\nperturbation of the trial function, this method can used to systematically\nimprove the energy bounds with a local skilled analysis; an algorithm relying\non this method can therefore be constructed and an explicit example for a\none-dimensional problem is given.",
    "arxiv_id": "quant-ph/0412121",
    "authors": [
      "Amaury Mouchet"
    ],
    "categories": [
      "quant-ph",
      "math.SP",
      "nlin.CD"
    ],
    "doi": "10.1088/0305-4470/38/5/006",
    "journal_ref": "Journal of Physics A 38 (2005) 1039",
    "title": "A differential method for bounding the ground state energy",
    "url": "https://arxiv.org/abs/quant-ph/0412121"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f0626e3f-1163-417d-aa7d-d10e28b76339",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}