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The Schrödinger equation and a multidimensional inverse scattering transform

✍ Scribed by Swanhild Bernstein

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
113 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The Schrödinger equation is one of the most important equations in mathematics, physics and also engineering. We outline some connections between transformations of non‐linear equations, the Schrödinger equation and the inverse scattering transform. After some remarks on generalizations into higher dimensions we present a multidimensional ∂¯ method based on Clifford analysis. To explain the method we consider the formal solution of the inverse scattering problem for the n‐dimensional time‐dependent Schrödinger equations given by A.I. Nachman and M.J. Ablowitz. Copyright © 2002 John Wiley & Sons, Ltd.

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