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Modern Physics Letters B 22 (2008) 2181
Using mixed data in the inverse scattering problem
M. Lassaut1, S. Y. Larsen2, S. A. Sofianos3, J-C. Wallet4

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 $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$, 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.
1 :  IPNO - Institut de Physique Nucléaire d'Orsay
2 :  Department of Physics
3 :  Physics Department
4 :  LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
Mathématiques/Physique mathématique

Physique/Physique mathématique

Physique/Physique des Hautes Energies - Théorie
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