A Stationary Analysis of Resonance States

Expansion of localized functions in terms of scattering states 

Looking now at the expansion in Eq. (4), the wave packet ir x,t) will contain contributions from these two groups of continuum eigenstates, which will depend on the expansion coefficients C(E) given in Eq. (5) and can now be separated to 

With this somewhat artificial separation, we can recast Eq. (4) as 

Even though we have a continuous superposition of states in Section 2, we observed in the interaction region the behavior of a stationary state, which 

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