Minimal velocity bound for Schroedinger-type operator with fractional powers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866912176837492736 |
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| author | Ishida, Atsuhide |
| author_facet | Ishida, Atsuhide |
| contents | It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the two-body Schroedinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities. Our estimates are expected to be applied to prove the asymptotic completeness for the fractional Schroedinger-type operators in various (not only short-range but also long-range and N-body) situations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05388 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Minimal velocity bound for Schroedinger-type operator with fractional powers Ishida, Atsuhide Mathematical Physics It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the two-body Schroedinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities. Our estimates are expected to be applied to prove the asymptotic completeness for the fractional Schroedinger-type operators in various (not only short-range but also long-range and N-body) situations. |
| title | Minimal velocity bound for Schroedinger-type operator with fractional powers |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2007.05388 |