Inverse Schrödinger Scattering in Three Dimensions

  • Roger G. Newton

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

Table of contents

  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

About this book

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

  • Roger G. Newton
    • 1
  1. 1.Department of PhysicsIndiana UniversityBloomingtonUSA

Bibliographic information

  • 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 Springer Book Archive
  • Print ISBN 978-3-642-83673-2
  • Online ISBN 978-3-642-83671-8
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site