Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915617171308544 |
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| author | Ishida, Atsuhide |
| author_facet | Ishida, Atsuhide |
| contents | We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians 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 Schroedinger operator and the time-independent repulsive Hamiltonians 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type Ishida, Atsuhide Analysis of PDEs We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians 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 Schroedinger operator and the time-independent repulsive Hamiltonians 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. |
| title | Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.05915 |