Transmission eigenvalues for the selfadjoint Schrödinger operator on the half line

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.

39 pages

References in corpus (1)

• Inverse scattering for vowel articulation with frequency-domain data

Cited by in corpus (2)

• Inverse problems for selfadjoint Schrödinger operators on the half line with compactly-supported potentials
• Inverse problem with transmission eigenvalues for the discrete Schrödinger equation