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On the imaginary part of coupling resonance points

Azamov Nurulla, Daniels Tom

Opuscula Mathematica

2019

Vol. 39, no. 5

611--621

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.