Inverse problem of scattering theory for a class one-dimensional Schrödinge equation

In this work, direct and inverse scattering problem on the real axis for the Schr¨odinger equation with piecewise-constant coefficient are studied. Using the new integral representations for solutions, the scattering data is defined, the main integral equations of the inverse scattering problem are obtained, the spectral characteristics of the scattering data are investigated and uniqueness theorem for the solution of inverse problem is proved. Key words: Schrödinger equation, scattering data, Jost solution, integral representation, inverse scattering problem