From what I have seen, Fermi's Golden rule is applied to constant or sinusoidal time varying potentials. But what if the perturbation is of the form [itex]V_0\left( \mathbf{x}\right)f\left(t\right)[/itex], where [itex]f(t)[/itex] is not a constant or sinusoidal? I am not really familiar with the derivation of Fermi's golden rule, and the explanations I was given both seemed very hand-wavy. I know we can Fourier decompose [itex]f(t)[/itex] in time, but it's not clear to me how that might be related back to transition probabilities. In particular, what if [itex]f(t) = e^{-a t}[/itex] with [itex]a \in \mathbb{R}, a > 0[/itex] ?(adsbygoogle = window.adsbygoogle || []).push({});

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# Fermi's Golden Rule: non-sinusoidal [itex]t\to\infty[/itex]

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