Are absorbed photons sinusoidal or sharp? Probably this has an obvious answer but I did not manage to find it...
When a photon of the appropriate frequency excites an atom, causing an electron transition, it acts as a “driving force”. In doing so, does it behave as a “sinusoidal” driving force or rather as a “sharp impulse”? If the answer is the latter, does it act as a (non-repetitive) delta function or a (periodic) Dirac comb?
 A: I'm guessing the "sharpness" you're alluding to - rather like the persistent, but in many ways inaccurate, notion of a quantum "leap" or "jump" is a manifestation of nonunitary quantum measurement; see also the companion discussion of the quantum measurement problem. 
When the quantum system you refer to is undisturbed ("unmeasured" or "unobserved"), it comprises a one-photon state of the electromagetic field coupled with the electronic states in question of the atom in question. The one photon electromagnetic field state can be any one photon state - totally delocalized (a plane, sinusoidal wave), somewhat localized, "sharp" whatever. But the coupled system's quantum state evolves smoothly with time, changing significantly, in this case, over time scales that are typically of the order of nanoseconds (for the case of allowed transitions). I say more about this smooth evolution in this answer here.
But when you observe the atom - or, more precisely, detect its emitted light - you're making measurement (usually in this case with a photodetector) with a "sharp" yes / no answer: the atom has / hasn't already absorbed / emitted the light in question. You can see that the "sharpness" comes wholly from quantum measurement.
The electromagnetic field unitary state can be as "sharp" or as "smooth" as you like: its simply that its initial state governs the probability distribution of when the photodetector is going to detect the transition. If the EM state is "smooth", spread out, sinusoidal and delocalized, then you will observe a wide variety of detection times as you repeat your measurement. More "bunched up" EM field states will lead to a narrower probability distribution of detection times.
