On the unitarity of S-matrix in 1-d case

Abstract

It is shown that the scattering S-matrix is unitary even if the scattering potential U(x) tends to different limits at plus and minus infinity. This result is in contrast to the statements of some authors which argue that the different potential values at infinity can break unitarity. The mistake may result from a wrong normalization of the wave functions. This work may be considered as a comment to some of those works.