# Accession Number:

## AD0287908

# Title:

## THE THREE-DIMENSIONAL INVERSE SCATTERING PROBLEM

# Descriptive Note:

## Research rept.

# Corporate Author:

## NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1962-07-01

# Pagination or Media Count:

## 45.0

# Abstract:

A concrete form for the mathematical theory of an inverse scattering problem is presented which was originally formulated in quantum mechanical terms. The problem is related to determining the variation of electron density in an ionized gas such as the earths ionosphere by means of radio sounding experiment s he definitions and proofs of theorems have been revised in an attempt to take the analysis understandable to a reader we may not be familiar with the terminology of quantum mechanics or of the associated HILBERT SPACE THEORY. While the usual terminology employed by physicist has not been discarded completely, definitions and relations are given in concrete terms whenever possible, and abstract relations reused for convenience of notation rather than for the purpose of obtaining great generality. The physical problem at which the present work is aimed is to find the variation of electron density in a weakly ionized gas from a knowledge of the scattering amplitude resulting from the incidence of a plane electromagnetic wave. It is assumed that the relevant properties of the medium vary slowly enough so that a scalar wave describes the scattering phenomena with sufficient accuracy. it is also assumed that losses, ordinarily attributed to the collisions of the electrons with heavy particles may be neglected. The effect of an external magnetic field which would cause anisotropy is neglected as well, so that the scattering is assumed to be isotropic as well as losses.

# Subject Categories:

- Quantum Theory and Relativity
- Radiofrequency Wave Propagation