Transmission eigenvalues for the selfadjoint Schr\"odinger operator on the half line
Spectral Theory
2016-10-06 v1
Abstract
The transmission eigenvalues corresponding to the half-line Schr\"odinger 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.
Cite
@article{arxiv.1404.2379,
title = {Transmission eigenvalues for the selfadjoint Schr\"odinger operator on the half line},
author = {Tuncay Aktosun and Vassilis G. Papanicolaou},
journal= {arXiv preprint arXiv:1404.2379},
year = {2016}
}
Comments
39 pages