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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Mathematical theory of single channel systems. Analyticity of scattering matrix


Author: I. M. Sigal
Journal: Trans. Amer. Math. Soc. 270 (1982), 409-437
MSC: Primary 35P25; Secondary 47A40, 81F10
DOI: https://doi.org/10.1090/S0002-9947-1982-0645323-X
MathSciNet review: 645323
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Abstract: We show that the $ S$-matrix of a quantum many-body, short-range, single-channel system has a meromorphic continuation whose poles occur at most at the dilation-analytic resonances [28], [24] and at the eigenvalues of the Hamiltonian. In passing, we prove the main spectral theorem (on location of the essential spectrum) and asymptotic completeness for the mentioned class of systems.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0645323-X
Article copyright: © Copyright 1982 American Mathematical Society