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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)

Abstract

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.

Keywords

Asymptotic Behavior Entire Function Input Function Matrix Method Scattering Amplitude 
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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