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 H0 and considering the time-dependent perturbation
$V(t)=\begin{cases} V(\underline{r}),& \mbox{if } t_i
where tf−ti is the interval of interaction, and then considering the limit for ti→−∞, tf→+∞. Now, what is the range of validity of this approximation?
Answer
...the assumption that the time of the measurement is much larger than the time needed for the transition...
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