Mathematical theory of single channel systems. Analyticity of scattering matrix

Sigal, I. M.

doi:10.1090/S0002-9947-1982-0645323-X

Mathematical theory of single channel systems. Analyticity of scattering matrix
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Trans. Amer. Math. Soc. 270 (1982), 409-437 Request permission

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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