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Multidimensional Inverse Quantum Scattering Problem and Wiener-Hopf Factorization

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Inverse Methods in Action

Part of the book series: Inverse Problems and Theoretical Imaging ((IPTI))

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Abstract

We consider the direct and inverse scattering for the n-dimensional Schrodinger equation, n ≥ 2, with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem, which plays a key role in inverse scattering.

Research supported in part by the NSF grant DMS-8823102

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, 75083, USA

    T. Aktosun

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    C. van der Mee

Authors
  1. T. Aktosun
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  2. C. van der Mee
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Editor information

Editors and Affiliations

  1. Laboratoire de Physique Mathématique, Université des Sciences et Techniques du Languedoc, Place Eugène Bataillon, F-34060, Montpellier Cedex, France

    Pierre C. Sabatier

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© 1990 Springer-Verlag Berlin Heidelberg

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Aktosun, T., van der Mee, C. (1990). Multidimensional Inverse Quantum Scattering Problem and Wiener-Hopf Factorization. In: Sabatier, P.C. (eds) Inverse Methods in Action. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75298-8_30

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  • DOI: https://doi.org/10.1007/978-3-642-75298-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75300-8

  • Online ISBN: 978-3-642-75298-8

  • eBook Packages: Springer Book Archive

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