Virginia TechAktosun, T.Klaus, Martinvan der Mee, Cornelis2014-04-092014-04-091993-07Aktosun, T.; Klaus, M.; Vandermee, C., "On the Riemann–Hilbert problem for the one dimensional Schrödinger equation," J. Math. Phys. 34, 2651 (1993); http://dx.doi.org/10.1063/1.5300890022-2488http://hdl.handle.net/10919/47073A matrix Riemann-Hilbert problem associated with the one-dimensional Schrodinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this Riemann-Hilbert problem yields the solution of the inverse scattering problem for a larger class of potentials than the usual Faddeev class. Some examples of explicit solutions of the Riemann-Hilbert problem are given, and the connection with ambiguities in the inverse scattering problem is established.en-USIn Copyrightinverse scatteringlineArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/34/7/10.1063/1.530089https://doi.org/10.1063/1.530089