{
  "abstract": "A singular sextic oscillator in the finite-Hermite biconfluent-Heun hierarchy generates an exact four-member power-Liouville Hermite orbit. Power coordinate transformations with the Liouville amplitude map the hierarchy member $N=4$ to four half-line Schrödinger spectral charts while preserving the physical regular-recessive Wronskian zero set under energy-coupling reparametrization. Two charts are the previously studied $x^{2/3}$ and inverse-square-root conditionally integrable potentials; the orbit embeds this known power-dual pair together with the singular sextic and linear-plus-quadratic charts. On the selected physical slice, the degree-five accessory compatibility obstruction vanishes identically, while the transformed Frobenius index reproduces both published fractional-power centrifugal coefficients. The common endpoint condition yields an exact discrete sequence of quartic Sturmian eigencouplings for the sextic oscillator. Independent two-sided shooting confirms representative eigencouplings and node counts. A matched large-action analysis further derives the first matched-endpoint correction within the leading Langer action and improves the Maslov-shifted effective-level approximation. The construction thus connects exact Hermite solvability, energy quantization, coupling quantization, and power duality within a single spectral orbit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11533",
  "author_total": 2,
  "authors": [
    {
      "name": "Artur Ishkhanyan"
    },
    {
      "name": "Miloslav Znojil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zyzz623g4bht.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11533",
  "fulltext_url": null,
  "id": "4zyzz623g4bht",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11533",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.11533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zyzz623g4bht.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11533"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Power-Liouville Hermite Orbit: Common Spectral Quantization of the Singular Sextic Oscillator and Fractional-Power Potentials",
  "title_text": "A Power-Liouville Hermite Orbit: Common Spectral Quantization of the Singular Sextic Oscillator and Fractional-Power Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/4zyzz623g4bht",
  "venue": "arXiv",
  "versions": []
}