Inverse scattering on the line with incomplete scattering data
数学物理
2007-05-23 v1 math.MP
摘要
The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a corresponding reflection coefficient to the transmission coefficient. It is shown that there are a discrete number of potentials corresponding to the data and that their L^2-norms are related to each other in a simple manner. All those potentials are identified, and it is shown how an additional estimate on the L^2-norm in the data can uniquely identify the corresponding potential. The recovery is illustrated with some explicit examples.
引用
@article{arxiv.math-ph/0402021,
title = {Inverse scattering on the line with incomplete scattering data},
author = {Tuncay Aktosun},
journal= {arXiv preprint arXiv:math-ph/0402021},
year = {2007}
}
备注
11 pages, to appear in Contemporary Mathematics