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In developing Fermi's Golden Rule, 2 approximations are made:

(1)

The energy interval E (continuum) to which discrete states are scattered is small enough such that the density of states is constant in this interval.

(2)

The time t is large enough such that the energy interval E is greater than the Bohr frequency. E >> 2 pi h / t

(h is h-bar!!!)

Now I do not get this 2nd one.

There is a factor involving cosine of (w.t), where w is the Bohr frequency connecting the final and initial states. For small t, this factor oscillates rapidly and has a peak when the 2 states are equal, showing that scattering that preserves the unperturbed energy is dominant. This bit is clear.

Yet why must the energy interval be greater than the Bohr f?? An what does this have to do with time? The Bohr f is really just an energy difference right? I dont see how the inequality from (2) arises, or why it is important?