Inverse problem on the line without phase information. (English) Zbl 0902.34011

The paper is devoted to the recovery of a potential with support on a right half-time, in terms of scattering data consisting of values of reflection coefficients. A known potential is placed to the left of the unknown potential and a value of the reflection coefficient of the combined potential constitutes the basic data. More precisely, the authors consider the inverse scattering problem when the data consist of values of the reflection coefficients, for potentials for which there are no bound states, so that the unknown potential can be determined provided one can find phases of the reflection coefficients. Several methods are described for the retrieval. It is supplemented with illustrative examples.


34A55 Inverse problems involving ordinary differential equations
81U40 Inverse scattering problems in quantum theory
Full Text: DOI Link