The Three-Dimensional Inverse Problem

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


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


Schrodinger Equation Exceptional Point Classical Wave Symmetric Kernel Chapter Xvii 
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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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