Virginia TechAktosun, T.Klaus, Martinvan der Mee, Cornelis2014-04-092014-04-091992-05Aktosun, T.; Klaus, M.; Vandermee, C., "Scattering and inverse scattering in one-dimensional nonhomogeneous media," J. Math. Phys. 33, 1717 (1992); http://dx.doi.org/10.1063/1.5296500022-2488http://hdl.handle.net/10919/47081The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrodinger equation d2-psi/dx2 + k2-psi = k2P(x)psi + Q(x)psi with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the scattering matrix are obtained; the inverse scattering problem of recovering the restoring force when the wave speed and the scattering data are known are also solved.en-USIn Copyrightschrodinger-equationlineArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/33/5/10.1063/1.529650https://doi.org/10.1063/1.529650