Introduction to Schrödinger inverse scattering

Abstract

Schrödinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q( x), which tend to zero as | x| → ∞. Inverse scattering for isolated impurities in backgrounds p( x) that are periodic, are Heaviside steps, are constant for x > 0 and periodic for x < 0, or that tend to zero as x → ∞ and tend to ∞ as x → -∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length.