Properties of the stationary resonance state

From this equation, we see that the particles in such a stationary state will be escaping the interaction region with momentum kr as can be verified by 

The Siegert resonance state provides a method of calculating the lifetime and position of the decaying state without the need to solve the TDSE. Aside from the practical advantage, they also greatly facilitate the understanding 

We can use any of the above mentioned techniques to find the resonance solutions of the TISE for the model potential presented in the previous section. Doing so, we find that there is a resonance solution at the complex energy (in atomic units)  

This is the resonance solution with the smallest position, i.e., smallest real part of the complex energy. Comparing this result with the measurements from the time-dependent simulation in Section 2, the agreement is truly remarkable. The corresponding momentum kres, 

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