We consider the whole-line inverse scattering problem for Sturm-Liouville equations which have constant coefficients on a half-line. Since in this case the reflection coefficient determines a Weyl-Titchmarsh m-function, it determines the coefficients up to some simple Liouville transformations. Given inverse spectral theory, proofs are fairly simple but provide extensions of known results as we require less smoothness and less decay than is customary. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
