INVERSE SCATTERING FOR THE ONE DIMENSIONAL SCHRDINGER EQUATION WITH THE ENERGY DEPENDENT POTENTIAL AND DISCONTINUTY CONDITIONS
Vol. 8(2) July 2020, No. 18, pp. 198-208
A.ADILOGLU NABIEV AND R.KH. AMIROV
Abstract
This work studies the direct and inverse scattering problems on the real axis for the one dimensional Schrˆdinger equation with the potential linearly dependent on the spectral parameter and with the discontinuity conditions at some point. Using the integral representations of the Jost solutions it is investigated the properties of the scattering data, obtained the main integral equations of the inverse scattering problem and the uniqueness theorem for recovering of the potential functions is proved.