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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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