@Article{Azamov2019,
author = "Azamov, Nurulla and Daniels, Tom",
title = "On the imaginary part of coupling resonance points",
journal = "Opuscula Math.",
year = "2019",
volume = "39",
number = "5",
pages = "611--621",
doi = "https://doi.org/10.7494/OpMath.2019.39.5.611",
url = "https://doi.org/10.7494/OpMath.2019.39.5.611",
abstract = "We prove for rank one perturbations that the imaginary part of a coupling resonance point is inversely proportional by a factor of \(-2\) to the rate of change of the scattering phase, as a function of the coupling variable, evaluated at the real part of the resonance point. This equality is analogous to the Breit-Wigner formula from quantum scattering theory. For more general relatively trace class perturbations, we also give a formula for the spectral shift function in terms of coupling resonance points, non-real and real.",
keywords = "scattering matrix, scattering phase, resonance point, Breit-Wigner formula",
issn = "1232-9274"
}