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Inverse source problem for the 1D Schrödinger equation

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The inverse problem of determining a source in the dynamical Schrödinger equation iu t  − u xx  + q(x) = w(t)a(x), 0 < x < 1, with zero Dirichlet boundary conditions and zero initial condition, is considered. From the measurement of u x (0, t), 0 < t < T, the unknown source a (x) is recovered, provided that q(x) and w(t) are given. Also, it is described how one can recover a (x) and q (x) simultaneously from measurements at both boundary points. Bibliography: 16 titles.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Alaska Fairbanks, Alaska, USA

    S. A. Avdonin

  2. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    V. S. Mikhaylov

Authors
  1. S. A. Avdonin
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  2. V. S. Mikhaylov
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Correspondence to S. A. Avdonin.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 393, 2011, pp. 5-11.

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Avdonin, S.A., Mikhaylov, V.S. Inverse source problem for the 1D Schrödinger equation. J Math Sci 185, 513–516 (2012). https://doi.org/10.1007/s10958-012-0933-x

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  • DOI: https://doi.org/10.1007/s10958-012-0933-x

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