Inverse scattering on the line with incomplete scattering data
Abstract
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^2norms 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^2norm in the data can uniquely identify the corresponding potential. The recovery is illustrated with some explicit examples.
 Publication:

arXiv eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:mathph/0402021
 Bibcode:
 2004math.ph...2021A
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 34A55;
 81U40;
 34L25;
 34L40;
 47A40;
 8105
 EPrint:
 11 pages, to appear in Contemporary Mathematics