{
  "abstract": "We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise convergent series in the basis elements. The expansion coefficients of the series are orthogonal polynomials in the energy that satisfy the resulting three-term recursion relation starting with two-parameter initial values. These polynomials contain all physical information about the system and they depend on the values of the two parameters. We obtain the associated two-parameter potential function induced by the change in the initial values that causes the system's wavefunction to change. We give several illustrative examples of these systems with continuous and/or discrete energy spectra. Moreover, a curious phenomenon is observed where bound states and/or resonances are induced in a system with pure continuous spectrum (e.g., a free particle) if the two parameters in the initial values exceed certain critical limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Int. J. Mod. Phys. A 41 (2026) 2650154",
  "arxiv": "2605.09812",
  "author_total": 1,
  "authors": [
    {
      "name": "A. D. Alhaidari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ceatm5qef1p4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.09812",
  "fulltext_url": null,
  "id": "5ceatm5qef1p4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.09812",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.09812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ceatm5qef1p4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2605.09812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.09812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Two-parameter classes of exactly solvable quantum systems",
  "title_text": "Two-parameter classes of exactly solvable quantum systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/5ceatm5qef1p4",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1142/s0217751x2650154x",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}