# Fredholm determinants and inverse scattering problems

@article{Dyson1976FredholmDA, title={Fredholm determinants and inverse scattering problems}, author={Freeman J. Dyson}, journal={Communications in Mathematical Physics}, year={1976}, volume={47}, pages={171-183} }

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.

## 159 Citations

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