Abstract
Abstract
We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using the method of known background scatterers. In particular, in dimension d ⩾ 2, we show that |f
1|2 at high energies uniquely determines v via explicit formulas, where f
1 is the scattering amplitude for v + w
1, w
1 is an a priori known nonzero background scatterer, under the condition that supp v and supp w
1 are sufficiently disjoint. If this condition is relaxed, then we give similar formulas for finding v from |f|2, |f
1|2, where f is the scattering amplitude for v. In particular, we continue studies of Novikov (2016 J. Geom. Anal.
26 346–59) and Leshem et al (2016 Nat. Commun.
7 1–6).
Funder
Russian Science Foundation
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
7 articles.
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