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Inverse scattering from mixed data
M. Lassaut1, S. Y. Larsen, S. A. Sofianos, J. C. Wallet2

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.
1 :  IPNO - Institut de Physique Nucléaire d'Orsay
2 :  LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
Mathématiques/Physique mathématique

Physique/Physique mathématique
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