Construction of potentials using mixed scattering data

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dc.creatorLassaut, M.
dc.creatorLarsen, S. Y.
dc.creatorSofianos, S. A.
dc.creatorWallet, J. C.
dc.date2007-10-18
dc.date2008-09-09
dc.date.accessioned2026-07-07T11:44:46Z
dc.date.available2026-07-07T11:44:46Z
dc.descriptionThe long-standing problem of constructing a potential from mixed scattering data is discussed. We first 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 energy is such that the $r_{n}(E)$'s range from zero to infinity. The latter method is applied to the domain $\{E \geq E_0, \ell=\ell_0 \} \cup \{E=E_0, \ell \geq \ell_0 \}$ for which the zeros of the regular solution are monotonic in both parts of the domain and still range from zero to infinity. Our analysis suggests that a unique potential can be obtained from the mixed scattering data $\{δ(\ell_0,k), k \geq k_0 \} \cup \{δ(\ell,k_0), \ell \geq \ell_0 \}$ provided that certain integrability conditions required for the fixed $\ell$-problem, are fulfilled. The uniqueness is demonstrated using the JWKB approximation.
dc.description17 pages, 2 figures. Improved version involving an expanded introduction and additional physical considerations
dc.identifierhttps://arxiv.org/abs/0710.3524
dc.identifierhttp://arxiv.org/abs/0710.3524
dc.identifierInverseProb.24:055014,2008
dc.identifierdoi:10.1088/0266-5611/24/5/055014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201666
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleConstruction of potentials using mixed scattering data
dc.typetext

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