Resonance pole
= Resonance pole
{title2=$E=E_R-i\Gamma/2,\quad\Gamma>0$}
A pole of the continued <scattering matrix> associated with outgoing boundary conditions and an unstable trapped state. A pole below the real energy axis gives time dependence $e^{-iE_Rt/\hbar}e^{-\Gamma t/(2\hbar)}$, so the probability lifetime is $\hbar/\Gamma$. Bound-state poles instead lie on the positive imaginary wavenumber axis and produce square-integrable decaying spatial waves.