  Whenever the Breit-Wigner amplitude appears in a calculation,there are many
instances (e.g., Fermi's two-level system and the Weisskopf-Wigner
approximation) where energy integrations are extended from the scattering
spectrum of the Hamiltonian to the whole real line. Such extensions are
performed in order to obtain a desirable, causal result. In this paper, we
recall several of those instances and show that substituting the Breit-Wigner
amplitude by the complex delta function allows us to recover such desirable
results without having to extend energy integrations outside of the scattering
spectrum.
