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arXiv · 0809.2903

Using mixed data in the inverse scattering problem

M. Lassaut·S. Y. Larsen·S. A. Sofianos·J-C. Wallet
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Abstract

Consider the fixed-$\ell$ 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 the energy is such that the $r_{n}(E)$ range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{δ(\ell_0,k), k \geq k_0 \} \cup \{δ(\ell,k_0), \ell \geq \ell_0 \}$, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way.

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M. Lassaut, S. Y. Larsen, S. A. Sofianos, J-C. Wallet. 2008-09-17. Using mixed data in the inverse scattering problem. https://doi.org/10.1142/s0217984908016960

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