It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial system in an eigenstate of the unperturbed Hamiltonian $H_0$ and considering the time-dependent perturbation

$V(t)=\begin{cases} V(\underline{r}),& \mbox{if } t_i<t<t_f \\ 0, & \mbox{otherwise} \end{cases}$

where $t_f-t_i$ is the interval of interaction, and then considering the limit for $t_i \rightarrow -\infty$, $t_f \rightarrow + \infty$. Now, what is the range of validity of this approximation?



...the assumption that the time of the measurement is much larger than the time needed for the transition...

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