A mathematical formulation of the Mahaux–Weidenmüller formula for the scattering matrix

This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. M...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-10, Vol.42 (41), p.415202-415202 (22)
Main Authors: Christiansen, T J, Zworski, M
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. Moreover, we bound the difference between the scattering matrix and an approximation of it computed using a finite rank approximation of the interaction matrix.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/41/415202