The determinant of the scattering matrix and its relation to the number of eigenvalues

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Abstract

For a large class of scattering systems we study the behavior of the determinant of the scattering matrix as a function on the spectrum of the unperturbed operator. The variation of this determinant is related to the number of eigenvalues due to the perturbation. This relation generalizes results of Levinson and others. The range of physical systems to which these results apply is thus considerably extended.

Original languageEnglish
Pages (from-to)114-134
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume64
Issue number1
DOIs
StatePublished - 1 Jun 1978
Externally publishedYes

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