An approximation formula in the inverse scattering problem

Academic Article


  • An approximate formula is given by which the potential Q(x) can be recovered with any accuracy if only the scattering data of the Schrödinger operator -Δ + Q(x) is known for some sufficiently high energy value k. Thus the scattering data for all k around k = ∞ is not needed in order to get a good approximate value for the potential. The main tools for the proof are an asymptotic formula for the S-matrix [Y. Saitō, J. Math. Phys. 25, 3105 (1984)] and the spectral decomposition theorem for the Schrödinger operator -Δ + Q(x) based on the limiting absorption principle. © 1986 American Institute of Physics.
  • Published In

    Digital Object Identifier (doi)

    Pubmed Id

  • 22082676
  • Author List

  • Saito Y
  • Start Page

  • 1145
  • End Page

  • 1153
  • Volume

  • 27
  • Issue

  • 4