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The inverse backscattering problem in three dimensions

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Abstract

This article is a study of the mapping from a potentialq(x) onR 3 to the backscattering amplitude associated with the Hamiltonian −Δ+q(x). The backscattering amplitude is the restriction of the scattering amplitudea(θ, ω, k), (θ, ω, k)εS 2×S 2×ℝ+, toa(θ,−θ, k). We show that in suitable (complex) Banach spaces the map fromq(x) toa(x/|x|, −x/|x|, |x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA

    G. Eskin & J. Ralston

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  1. G. Eskin
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  2. J. Ralston
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Communicated by B. Simon

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Eskin, G., Ralston, J. The inverse backscattering problem in three dimensions. Commun. Math. Phys. 124, 169–215 (1989). https://doi.org/10.1007/BF01219194

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  • DOI: https://doi.org/10.1007/BF01219194

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