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188宝金博页面版: Explicit Formulas and Global Uniqueness for Phaseless Inverse Scattering in Multidimensions

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内容提示: J Geom Anal (2016) 26:346–359DOI 10.1007/s12220-014-9553-7Explicit Formulas and Global Uniqueness for PhaselessInverse Scattering in MultidimensionsR. G. NovikovReceived: 31 December 2014 / Published online: 15 January 2015? Mathematica Josephina, Inc. 2015Abstract We consider phaseless inverse scattering for the Schr?dinger equationwith compactly supported potential in dimension d ≥ 2. We give explicit formulasfor solving this problem from appropriate data at high energies. As a corollary, wegive also...

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J Geom Anal (2016) 26:346–359DOI 10.1007/s12220-014-9553-7Explicit Formulas and Global Uniqueness for PhaselessInverse Scattering in MultidimensionsR. G. NovikovReceived: 31 December 2014 / Published online: 15 January 2015© Mathematica Josephina, Inc. 2015Abstract We consider phaseless inverse scattering for the Schrödinger equationwith compactly supported potential in dimension d ≥ 2. We give explicit formulasfor solving this problem from appropriate data at high energies. As a corollary, wegive also a global uniqueness result for this problem with appropriate data on a f i xedenergy neighborhood.Keywords Schrödinger equation · Scattering amplitude · Phaseless inversescatteringMathematics Subject Classif i cation 35J10 · 35P25 · 35R30 · 81U401 IntroductionWe consider the Schrödinger equation− ?ψ + v(x)ψ = Eψ, x ∈ R d , d ≥ 2, E > 0, (1.1)R. G. Novikov ( B )CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique,91128 Palaiseau, Francee-mail: novikov@cmap.polytechnique.frR. G. NovikovIEPT RAS, 117997 Moscow, RussiaR. G. NovikovMoscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia123

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