Multidimensional inverse scattering: An orthogonalization formulation

Publisher Website
Google Scholar
Abstract
The three‐dimensional Schrödinger equation inverse scattering problem is solved using an orthogonalization approach. The plane waves propagating in free space are orthogonalized with respect to an inner product defined in terms of a Jost operator. The resulting integral equation is identical to the generalized Gel’fand–Levitan equation of Newton, although the present derivation is simpler and more physical than that of Newton. Newton’s generalized Marchenko equation is derived from the defining integral equation for the Jost operator. These integral equations are shown to be solved by fast algorithms derived directly from the properties of their solutions. This paper thus presents a simple interpretation of Newton’s two integral equations, two fast algorithms for solving these integral equations, and relations between the various approaches. This is a generalization of previously obtained results, which are also reviewed here, for the one‐dimensional inverse scattering problem.

This publication has 15 references indexed in Scilit: