TY  - JOUR
ID  - Azamov2019
LB  - Azamov2019
AU  - Azamov, Nurulla
AU  - Daniels, Tom
TI  - On the imaginary part of coupling resonance points
ST  - On the imaginary part of coupling resonance points
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 5
SP  - 611
EP  - 621
DO  - https://doi.org/10.7494/OpMath.2019.39.5.611
UR  - https://doi.org/10.7494/OpMath.2019.39.5.611
AB  - 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.
KW  - scattering matrix
KW  - scattering phase
KW  - resonance point
KW  - Breit-Wigner formula
SN  - 1232-9274
ER  -