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Multidimensional Inverse Scattering for the Schrödinger Equation

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Mathematical Analysis, its Applications and Computation (ISAAC 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 385))

Abstract

We give a short review of old and recent results on the multidimensional inverse scattering problem for the Schrödinger equation. A special attention is paid to efficient reconstructions of the potential from scattering data which can be measured in practice. In this connection our considerations include reconstructions from non-overdetermined monochromatic scattering data and formulas for phase recovering from phaseless scattering data. Potential applications include phaseless inverse X-ray scattering, acoustic tomography and tomographies using elementary particles. This paper is based, in particular, on results going back to M. Born (1926), L. Faddeev (1956, 1974), S. Manakov (1981), R. Beals, R. Coifman (1985), P. Grinevich, R. Novikov (1986), G. Henkin, R. Novikov (1987), and on more recent results of R. Novikov (1998–2019), A. Agaltsov, T. Hohage, R. Novikov (2019).

This paper is an extended version of the talk given at the 12th ISAAC Congress, Aveiro, Portugal, 29 July–2 August, 2019.

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Authors and Affiliations

  1. CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

    Roman G. Novikov

  2. IEPT RAS, Moscow, Russia

    Roman G. Novikov

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  1. Roman G. Novikov
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Correspondence to Roman G. Novikov .

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  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institute of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

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Novikov, R.G. (2022). Multidimensional Inverse Scattering for the Schrödinger Equation. In: Cerejeiras, P., Reissig, M. (eds) Mathematical Analysis, its Applications and Computation. ISAAC 2019. Springer Proceedings in Mathematics & Statistics, vol 385. Springer, Cham. https://doi.org/10.1007/978-3-030-97127-4_3

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