{
  "abstract": "We derive eigenstate comparisons from ordered Schrödinger operators, extending energy bounds to overlaps, spatial distributions and nodes. For three form-ordered operators with discrete comparison ground states, suppose the upper ground-state energy lies in the lower operator's ground-state gap. Three comparison spectral values then bound all three squared ground-state overlaps and guarantee a simple discrete intermediate ground state. Related gap estimates control low-energy subspaces and individual excited-state overlaps under additional gap conditions. In one dimension and radially, a single crossing of the potential difference relative to the energy shift orders ground-state likelihood ratios and monotone observables; a nondecreasing difference suffices. The results cover asymmetric wells and shortened right Dirichlet walls, with coordinatewise comparisons for submodular reference potentials and coordinatewise nondecreasing perturbations. A two-sided Sturm argument orders corresponding internal nodes for nondecreasing potential differences, even between orthogonal one-dimensional excited states. For Yukawa ground states, Hulthén comparisons bound overlaps, radial moments and the density at the nucleus; the latter two-sided bounds hold for screening $0<δ<2/\\sqrt6$. Optimizing scaled Hulthén majorants gives a lower bound of approximately $1.13611$ for $n^2δ_c(n,0)$, where $δ_c(n,0)$ is the critical screening for the $n$th $s$-wave bound state. This bound is optimal within that two-parameter comparison family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39136",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiao-Ke Wang"
    },
    {
      "name": "Han Jia"
    },
    {
      "name": "Shengjun Wu"
    },
    {
      "name": "Zeng-Bing Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0qp9gfqrmzkmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39136",
  "fulltext_url": null,
  "id": "0qp9gfqrmzkmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39136",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0qp9gfqrmzkmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Beyond energy bounds: comparing Schrödinger eigenstates",
  "title_text": "Beyond energy bounds: comparing Schrödinger eigenstates",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0qp9gfqrmzkmj",
  "venue": "arXiv",
  "versions": []
}