Quote by M Quack
Note the formula they give,
[itex]\omega_{\mathrm{rec}} = \frac{\hbar k^2}{2m} \ll \Gamma[/itex]
If you multiply both sides (all 3 sides :) ) by [itex]\hbar[/itex], the formula compares 3 energies.
[itex]\frac{\hbar^2 k^2}{2m}[/itex] is a kinetic energy
[itex]\hbar \omega[/itex] is the energy of an oscillator or wave (written as such to derive a characteristic time scale from the energy)
[itex]\hbar \Gamma[/itex] is the width of an emission line (for example), which is finite because of the finite life time of the initial state.

Ah, thanks for making that clear.
Quote by M Quack
adiabatic in this context means without transfer of energy.

I have to admit I still don't fully understand "adiabatic" in this context. So the internal dynamics follows the external COMmotion without any energy transfer(?). I'm not even sure I know what that means.
Does it refer to the fact that the spontaneously emitted photons (characterized by [itex]\Gamma^{1}[/itex]) are emitted *much* faster than the atom moves, so their effect is zero on average since they are emitted so often?
Thanks in advance.
Best regards,
Niles.