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arXiv · 2503.22811

Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type

Pei-Cheng Kuo·Roman G. Novikov
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Abstract

We consider the Schr\"odinger 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.

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Pei-Cheng Kuo, Roman G. Novikov. 2025-03-28. Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type. https://arxiv.org/abs/2503.22811

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