Inverse Problems in Quantum Scattering Theory pp 323-388 | Cite as

# Inverse Problems in One Dimension

## Abstract

*x*< ∞ is known to have some fundamental differences from scattering in three dimensions, and its radial one-dimensional counterpart on the half-line 0 ≤

*r*< ∞. It has given rise to numerous studies because of its applications in many electrical engineering problem, among which we may mention:

- 1.
Nonuniform transmission line in which either the inductance or the capacitance is constant, and in which we would like to reconstruct the line from the knowledge of the reflection coefficient

*r*(ω) supposed to be known for all frequencies. - 2.
Under certain conditions, the reconstruction of a waveguide of variable cross section from some part of the scattering matrix, usually the reflection coefficient.

- 3.
The problem in which a variable stratified dielectric is to be constructed so that the reflection coefficient of an electromagnetic wave will vary in a prescribed way with frequency.

- 4.
Determination of the ionization density of a stratified ionosphere from the time delay of a pulse radio wave which has been transmitted from the earth and reflected back to the earth by the ionosphere.

## Keywords

Inverse Problem Reflection Coefficient Real Axis Direct Problem Darboux Transformation## Preview

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