Skip to Main content Skip to Navigation
Journal articles

Construction of potentials using mixed scattering data

Abstract : The 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, rn(E) which are monotonic functions of the energy, determine a unique potential when the domain of energy is such that the rn(E)'s range from zero to infinity. The latter method is applied to the domain {E ≥ E0, ell = ell0} ∪ {E = E0, ell ≥ ell0} 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(ell0, k), k ≥ k0} ∪ {δ(ell, k0), ell ≥ ell0} provided that certain integrability conditions required for the fixed ell problem, are fulfilled. The uniqueness is demonstrated using the JWKB approximation.
Document type :
Journal articles
Complete list of metadatas

http://hal.in2p3.fr/in2p3-00422016
Contributor : Sophie Heurteau <>
Submitted on : Tuesday, October 6, 2009 - 10:26:25 AM
Last modification on : Wednesday, September 16, 2020 - 4:07:54 PM

Links full text

Identifiers

Collections

Citation

M. Lassaut, S. Y. Larsen, S.A. Sofianos, J. C. Wallet. Construction of potentials using mixed scattering data. Inverse Problems, IOP Publishing, 2008, 24, pp.055014. ⟨10.1088/0266-5611/24/5/055014⟩. ⟨in2p3-00422016⟩

Share

Metrics

Record views

148