Discretization of inverse scattering on a half line

Abstract

We solve inverse scattering problem for Schrödinger operators with compactly supported potentials on the half line. We discretize S-matrix: We take the value of the S-matrix on some infinite sequence of positive real numbers. Using this sequence obtained from S-matrix, we recover uniquely the potential by a new explicit formula, without the Gelfand-Levitan-Marchenko equation. K E Y W O R D S inverse scattering, Schrödinger operators M S C ( 2 0 2 0 ) 81Q10 (34L40 47E05 47N50)