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arXiv · 1404.2379

Transmission eigenvalues for the selfadjoint Schrödinger operator on the half line

Tuncay Aktosun·Vassilis G. Papanicolaou
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Abstract

The transmission eigenvalues corresponding to the half-line Schrödinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a transmission eigenvalue corresponds to the energy at which the scattering from the perturbed system agrees with the scattering from the unperturbed system. A corresponding inverse problem for the recovery of the potential from a set containing the boundary condition and the transmission eigenvalues is analyzed, and a unique reconstruction of the potential is given provided one additional constant is contained in the data set. The results are illustrated with various explicit examples.

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Tuncay Aktosun, Vassilis G. Papanicolaou. 2014-04-09. Transmission eigenvalues for the selfadjoint Schrödinger operator on the half line. https://doi.org/10.1088/0266-5611%2F30%2F7%2F075001

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