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Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type.

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Title: Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type.
Authors: Ishida, Atsuhide1 (AUTHOR) aishida@rs.tus.ac.jp
Source: Journal of Inverse & Ill-Posed Problems. Dec2025, Vol. 33 Issue 6, p845-859. 15p.
Subjects: Quantum scattering, Hamiltonian systems, Scattering (Mathematics), Coulomb potential, Quadratic forms
Abstract: We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonian of quadratic type. The time-dependent coefficient on the repulsive term decays as the inverse square of time, which is the threshold between the standard free Schrödinger operator and the time-independent repulsive Hamiltonian of quadratic type. Applying the Enss–Weder time-dependent method, we can determine uniquely the short-range potential functions with Coulomb-like singularities from the velocity limit of the scattering operator. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Inverse & Ill-Posed Problems is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 189664806
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type.
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  Data: <searchLink fieldCode="AR" term="%22Ishida%2C+Atsuhide%22">Ishida, Atsuhide</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aishida@rs.tus.ac.jp</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Inverse+%26+Ill-Posed+Problems%22">Journal of Inverse & Ill-Posed Problems</searchLink>. Dec2025, Vol. 33 Issue 6, p845-859. 15p.
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  Label: Abstract
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  Data: We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonian of quadratic type. The time-dependent coefficient on the repulsive term decays as the inverse square of time, which is the threshold between the standard free Schrödinger operator and the time-independent repulsive Hamiltonian of quadratic type. Applying the Enss–Weder time-dependent method, we can determine uniquely the short-range potential functions with Coulomb-like singularities from the velocity limit of the scattering operator. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Inverse & Ill-Posed Problems is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1515/jiip-2025-0026
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 845
    Subjects:
      – SubjectFull: Quantum scattering
        Type: general
      – SubjectFull: Hamiltonian systems
        Type: general
      – SubjectFull: Scattering (Mathematics)
        Type: general
      – SubjectFull: Coulomb potential
        Type: general
      – SubjectFull: Quadratic forms
        Type: general
    Titles:
      – TitleFull: Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type.
        Type: main
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          Name:
            NameFull: Ishida, Atsuhide
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          Dates:
            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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              Value: 09280219
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              Value: 33
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              Value: 6
          Titles:
            – TitleFull: Journal of Inverse & Ill-Posed Problems
              Type: main
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