  Scatterings of electrons at quasiparticles or photons are very important for
many topics in solid state physics, e.g., spintronics, magnonics or photonics,
and therefore a correct numerical treatment of these scatterings is very
important. For a quantum-mechanical description of these scatterings Fermi's
golden rule is used in order to calculate the transition rate from an initial
state to a final state in a first-order time-dependent perturbation theory. One
can calculate the total transition rate from all initial states to all final
states with Boltzmann rate equations involving Brillouin zone integrations. The
numerical treatment of these integrations on a finite grid is often done via a
replacement of the Dirac delta distribution by a Gaussian. The Dirac delta
distribution appears in Fermi's golden rule where it describes the energy
conservation among the interacting particles. Since the Dirac delta
distribution is a not a function it is not clear from a mathematical point of
view that this procedure is justified. We show with physical and mathematical
arguments that this numerical procedure is in general correct, and we comment
on critical points.
