Using mixed data in the inverse scattering problem

Details Using mixed data in the inverse scattering problem Using mixed data in the inverse scattering problem

2008-09-17

arxiv.org/abs/0809.2903v1

Mod. Phys. Lett. B22 (2008) 2181

Physics

Mathematical Physics

9 pages, 2 figures. Talk given at the Conference of Inverse Quantum Scattering Theory, Hungary, August 2007

Scientific paper

10.1142/S0217984908016960

Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger 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.

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