Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916665748357120 |
|---|---|
| author | Kuo, Pei-Cheng Novikov, Roman G. |
| author_facet | Kuo, Pei-Cheng Novikov, Roman G. |
| contents | We consider the Schrödinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy. Moreover, we show that there is no non-zero potential of this type with zero scattering amplitude at a fixed positive energy and a fixed incident direction. Nevertheless, we also show that a multipoint potential of this type is not uniquely determined by its scattering amplitude at a positive energy E and a fixed incident direction. Our proofs also contribute to the theory of inverse source problem for the Helmholtz equation with multipoint source. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type Kuo, Pei-Cheng Novikov, Roman G. Analysis of PDEs Mathematical Physics 35J05, 35J10, 35R30, 81U40 We consider the Schrödinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy. Moreover, we show that there is no non-zero potential of this type with zero scattering amplitude at a fixed positive energy and a fixed incident direction. Nevertheless, we also show that a multipoint potential of this type is not uniquely determined by its scattering amplitude at a positive energy E and a fixed incident direction. Our proofs also contribute to the theory of inverse source problem for the Helmholtz equation with multipoint source. |
| title | Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type |
| topic | Analysis of PDEs Mathematical Physics 35J05, 35J10, 35R30, 81U40 |
| url | https://arxiv.org/abs/2503.22811 |