Fredholm determinants and inverse scattering problems |
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Authors: | Freeman J. Dyson |
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Affiliation: | (1) Institute for Advanced Study, 08540 Princeton, N.J., USA |
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Abstract: | 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.Research sponsored by the National Science Foundation, Grant No. GP-40768X. |
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