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The Three-Dimensional Inverse Problem

  • K. Chadan
  • P. C. Sabatier
  • R. G. Newton
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

In a time-independent formulation of nonrelativistic scattering, one starts with the Schrödinger equation
$$(1 - i{\partial \over {\partial r}})K(r,r') = - ir'K\left( {r'} \right)\exp \left[ {ir} \right]\, + \,{K_N}\left( {r,r'} \right),$$
(XIV.1.1)
for the wave function Ψ, and one assumes that the properties of V(r) are sufficient to guarantee the following asymptotic form of Ψ:
$$\left. {\matrix{ \hfill {{K_N}\left( {r,r'} \right) \to 0} & \hfill {\,\left( {r \to \infty } \right),} \cr \hfill {\int_0^r {|{K_N}\left( {r,r'} \right)|{{\left[ {r'\left( {1 + r'} \right)} \right]}^{ - 1}}\,dr' \to 0} } & \hfill {\left( {r \to \infty } \right).} \cr } } \right\}$$
(XIV.1.2)

Keywords

Schrodinger Equation Exceptional Point Classical Wave Symmetric Kernel Chapter Xvii 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • K. Chadan
    • 1
  • P. C. Sabatier
    • 2
  • R. G. Newton
    • 3
  1. 1.Laboratoire de Physique ThéoriqueUniversité de Paris-SudOrsayFrance
  2. 2.Université des Sciences et Techniques du LanguedocMontpellier CedexFrance
  3. 3.Department of PhysicsIndiana UniversityBloomingtonUSA

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