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The inverse scattering problem for the 1‐D Schrodinger equation d2ψ/dx2 + k2ψ= k2P(x)ψ + Q(x)ψ is studied. This equation is equivalent to the 1‐D wave equation with speed 1/√1−P(x) in a nonhomogeneous medium where Q(x) acts as a restoring force. When Q(x) is integrable with a finite first moment, P(x)<1 and bounded below and satisfies two integrability conditions, P(x) is recovered uniquely when the scattering data and Q(x) are known. Some explicitly solved examples are provided.

Inverse scattering in 1-D nonhomogeneous media and recovery of the wave speed