{
  "abstract": "The initial-to-final-state inverse problem for the Schrödinger equation consists in determining uniquely the Hamiltonian that generates the evolution, assuming the knowledge of the initial-to-final-state map. This functional maps each initial state $f\\in L^2(\\mathbb{R}^n)$ to the corresponding final state at a fixed time $T$. The problem was formulated by Caro and Ruiz in the case of Hamiltonians arising from time-dependent bounded electric potentials that exhibit super-exponential decay at infinity. Caro, Parissis and the authors of this article established that uniqueness also holds for time-independent bounded potentials with super-linear decay at infinity. In this paper, we quantify the above uniqueness results establishing that the potentials are stable under small changes of the initial-to-final-state maps. In the case of time-dependent potentials we get a stability of logarithmic type. A notable improvement is achieved when the potentials are time-independent, where under this assumption we prove Hölder stability estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00257",
  "author_total": 2,
  "authors": [
    {
      "name": "Manuel Cañizares"
    },
    {
      "name": "Thanasis Zacharopoulos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmftp86bcd5kx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00257",
  "fulltext_url": null,
  "id": "fmftp86bcd5kx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00257",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7206195356",
  "pdf_url": "https://arxiv.org/pdf/2609.00257",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmftp86bcd5kx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00257",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00257"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability estimates for the initial-to-final-state inverse problem",
  "title_text": "Stability estimates for the initial-to-final-state inverse problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/fmftp86bcd5kx",
  "venue": "arXiv",
  "versions": []
}