Abstract
Using second-order, time-dependent perturbation theory, we calculate the intermediate and final state amplitudes for transitions from an initial to a final state via an intermediate resonance. When our complex energies are replaced by real energies our results are identical to the real energy final state amplitudes obtained by other authors, thus justifying the usual phenomenological replacement of real energies with complex ones when considering resonance behavior. We then derive the Fermi Golden Rule No. 1 with complex energies.
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