  Fermi's golden rule is of great importance in quantum dynamics. However, in
many textbooks on quantum mechanics, its contents and limitations are obscured
by the approximations and arguments in the derivation, which are inevitable
because of the generic setting considered. Here we propose to introduce it by
an ideal model, in which the quasi-continuum band consists of equaldistant
levels extending from $-\infty $ to $+\infty $, and each of them couples to the
discrete level with the same strength. For this model, the transition
probability in the first order perturbation approximation can be calculated
analytically by invoking the Poisson summation formula. It turns out to be a
\emph{piecewise linear} function of time, demonstrating on one hand the key
features of Fermi's golden rule, and on the other hand that the rule breaks
down beyond the \emph{Heisenberg time}, even when the first order perturbation
approximation itself is still valid.
