  The exact determination of the spontaneous emission coefficient for an
excited atom is an extremely complex problem so various approximations are
typically used. One of the most popular ones is the use of the dipole
approximation of a two-level atom followed by rotating wave approximation
(RWA). However, such an approach applied to the entire frequency spectrum
results in the appearance of divergent integrals in the derivations, which are
not treated rigorously in typical student textbooks. It is known from the
literature that the introduction of cutoff for frequencies, justified by the
finite size of the atom, may solve this problem. For didactic purposes, in this
paper, we introduce a mathematically simple cutoff, which allows for a
straightforward yet mathematically consistent rederivation of the
Weisskopf-Wigner spontaneous emission rate (up to the small correction) within
RWA. Importantly, this cutoff is not a mathematical trick to make calculations
easier but is related to a real feature of the physical system, the neglect of
which leads to inconsistency. More precise analysis demand going beyond RWA and
dipole approximation.
