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Inverse scattering from mixed data

Abstract : We first consider the fixed-$l$ inverse scattering problem. We show that the zeros of the regular solution of the Schrödinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of energy is such that the $r_{n}(E)$'s range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{\delta(l_0,k), k \geq k_0 \} \cup \{\delta(l,k_0), l \geq l_0 \}$, for which the zeros of the regular solution are monotonic in both domain and range from zero to infinity, offers the possibility of determining the potential in a unique way. This will be demonstrated in the JWKB approximation.
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http://hal.in2p3.fr/in2p3-00180881
Contributor : Suzanne Robert <>
Submitted on : Monday, October 22, 2007 - 12:18:09 PM
Last modification on : Wednesday, September 16, 2020 - 4:08:29 PM

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M. Lassaut, S. Y. Larsen, S. A. Sofianos, J. C. Wallet. Inverse scattering from mixed data. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2008, 24, pp.055014. ⟨10.1088/0266-5611/24/5/055014⟩. ⟨in2p3-00180881⟩

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