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Fermi's golden rule is of great importance in quantum dynamics. However, inmany textbooks on quantum mechanics, its contents and limitations are obscuredby the approximations and arguments in the derivation, which are inevitablebecause of the generic setting considered. Here we propose to introduce it byan ideal model, in which the quasi-continuum band consists of equaldistantlevels extending from $-\infty $ to $+\infty $, and each of them couples to thediscrete level with the same strength. For this model, the transitionprobability in the first order perturbation approximation can be calculatedanalytically by invoking the Poisson summation formula. It turns out to be a\emph{piecewise linear} function of time, demonstrating on one hand the keyfeatures of Fermi's golden rule, and on the other hand that the rule breaksdown beyond the \emph{Heisenberg time}, even when the first order perturbationapproximation itself is still valid.

Fermi's golden rule: its derivation and breakdown by an ideal model