Potentials from the Scattering Amplitude at Fixed Energy: Matrix Methods

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


The simplest way to introduce a function \(f_{{V_0}}^V(r,r')\) which is a solution of (XI.3.1) and which depends on a sequence of parameters {cμ} is to construct a linear combination of products \(\varphi _\mu ^{{V_0}}(r)\varphi _\mu ^{{V_0}}(r')\) with coefficients cμ. An alternative method might introduce products with strong consistency conditions. In all cases, a relation between {cμ} and {δl} must be found by investigating the asymptotic behavior of \(\varphi _l^V(r)\). This aim is achieved in the matrix methods we present in this chapter. They yield potentials in special classes that are defined by the nature of {μ}. We strictly limit our study to real potentials.


Asymptotic Behavior Entire Function Input Function Matrix Method Scattering Amplitude 
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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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