The Marchenko Method

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


The Levin representation is the analogue of the representation (III.1.8a), for the Jost solution f(k, r). We know from chapter I that this function is holomorphic in Im k > 0, and satisfies there, for r # 0, the bound (I.3.4). It follows from this that h = fe ikr is an L 2 function of k on any line parallel to the real axis, and that
$$\int_{ - \infty }^\infty {|h(\sigma + i\tau {|^2}d\sigma = O({e^{ - 2\tau r}})} {\rm{ }}{\rm{.}}$$


Integral Equation Inverse Problem Schrodinger Equation Chapter Versus Resolvent Kernel 
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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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