Connection Between Time- and Frequency-Domain Three-Dimensional Inverse Problems for the Schrödinger Equation
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Begun in 1973, the Review of Progress in Quantitative Nondestructive Evaluation (QNDE) is the premier international NDE meeting designed to provide an interface between research and early engineering through the presentation of current ideas and results focused on facilitating a rapid transfer to engineering development.
This site provides free, public access to papers presented at the annual QNDE conference between 1983 and 1999, and abstracts for papers presented at the conference since 2001.
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Abstract
The use of inverse scattering methods in electromagnetic remote sensing, seismic exploration and ultrasonic imaging is rapidly expanding. For these cases which involve classical wave equations with variable velocity,1 no exact inversion methods exists for general three-dimensional (3d) scatterers. However, exact inversion methods (for example, those based on the Born series2 and the Newton-Marchenko equation2) do exist for the 3d Schrödinger equation. In this paper, these inversion methods for Schrödinger’s equation will be rewritten in a form which brings out certain analogies with classical wave equations. It is hoped these analogies will eventually contribute to a common exact inversion method for both types of equations.