Inverse scattering with non-overdetermined data
نویسندگان
چکیده
منابع مشابه
Uniqueness theorem for inverse scattering problem with non-overdetermined data
Let q(x) be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data A(−β, β, k) ∀β ∈ S, ∀k > 0 determine q uniquely. MSC: 35P25, 35R30, 81Q05; PACS: 03.65.Nk
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Since the forties of the last century, the physicists were interested in the uniqueness of the determination of a physical system by its S-matrix. If the physical system is described by a Hamiltonian of the type H = −∇2 + q(x), then the S-matrix is in one-to-one correspondence with the scattering amplitude A, S = I + ik 2π A, where I is the identity operator and A is an operator in L2(S2) with ...
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Let q(x) be a real-valued compactly supported sufficiently smooth function. It is proved that the scattering data A(−β, β, k) ∀β ∈ S, ∀k > 0, determine q uniquely. Under the same assumptions on q(x) it is proved that the scattering data A(β, α0, k) ∀β ∈ S, ∀k > 0, and a fixed α0, the direction of the incident plane wave, determine q uniquely. The above scattering data are non-overdetermined in ...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2009
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2009.06.033