# Inverse Schrödinger Scattering in Three Dimensions

Book

Part of the Texts and Monographs in Physics book series (TMP)

1. Front Matter
Pages I-X
2. ### Introduction

1. Roger G. Newton
Pages 1-5
3. ### Use of the Scattering Solution

1. Front Matter
Pages 7-7
2. Roger G. Newton
Pages 8-43
3. Roger G. Newton
Pages 44-88
4. ### Use of the Regular and Standing-Wave Solutions

1. Front Matter
Pages 89-89
2. Roger G. Newton
Pages 90-99
3. Roger G. Newton
Pages 100-109
4. Roger G. Newton
Pages 110-116
5. ### Use of the Faddeev Solution

1. Front Matter
Pages 117-117
2. Roger G. Newton
Pages 118-137
3. Roger G. Newton
Pages 138-158
6. Back Matter
Pages 159-170

### Introduction

Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi­ ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti­ cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.

### Keywords

Potential angular momentum development direct scattering problem integral integral equation momentum paper scattering solution stability symmetry

#### Authors and affiliations

1. 1.Department of PhysicsIndiana UniversityBloomingtonUSA

### Bibliographic information

• Book Title Inverse Schrödinger Scattering in Three Dimensions
• Authors Roger G. Newton
• Series Title Texts and Monographs in Physics
• DOI https://doi.org/10.1007/978-3-642-83671-8
• Copyright Information Springer-Verlag Berlin Heidelberg 1989
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Hardcover ISBN 978-3-540-50563-1
• Softcover ISBN 978-3-642-83673-2
• eBook ISBN 978-3-642-83671-8
• Series ISSN 1864-5879
• Series E-ISSN 1864-5887
• Edition Number 1
• Number of Pages X, 170
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
Industry Sectors
Energy, Utilities & Environment