Unified Picture of Resonance States

In the previous sections, we have seen that a resonance can be described through both a time-dependent approach and a time-independent approach. The goal of this section is to create a unified picture that joins both methodologies and explain how general wave packets evolve into pseudostationary decaying states. 

Let us recap the properties of a wave packet populating a resonant state we observed in Section 2  

After some initial rearrangement time, a bound-like wavefunction is obtained in the interaction region. 

Outside the interaction region, one observes escaping particles with constant velocity. 

The probability to remain inside the interaction region decays exponentially with time. 

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