Fredholm determinants and inverse scattering problems

  title={Fredholm determinants and inverse scattering problems},
  author={Freeman J. Dyson},
  journal={Communications in Mathematical Physics},
  • F. Dyson
  • Published 1 June 1976
  • Mathematics
  • Communications in Mathematical Physics
The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two different types of Fredholm determinant. As an application of the method, an asymptotic formula of high accuracy is derived for a particular Fredholm determinant that determines the level-spacing distribution-function in the theory of random matrices. 
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