Does an excited state wave function depend on state preparation? Consider a quantum system with a ground state and many excited states (e.g. an atom).
If the system is in an excited state, to what extent does its wave function depend on the method of state preparation?  Does it matter if it was excited directly from the ground state versus an intermediate excited state?
Similarly, if the system is put in an excited state through a decay process (e.g. spontaneous emission), to what extent is its wave function different than if it had been put in that state through excitation (from the ground state or lower energy excited state)?
 A: Once a system is in a particular final state I cannot see anyway of finding out which state it came from. (I would be interested to hear about a way to do this if it was possible though.)
There are experiments though, where it is very important whether of not you pass through an intermediate state of not. - For example REMPI 
In Resonance Enhanced Multi Photon Ionization (REMPI) a molecule is excited first to an intermediate state and then it is ionized. The range and intensities of different final states observed in the experiment are strongly dependent on the intermediate state. - And the range and intensities final states observed in direct ionization from the ground state will almost always be very different. 
The point here is that as far as I can see the formation of a particular state does cannot tell you about the route (unless for example it is not possible from the ground state and only possible from an intermediate state).
By contrast, however, if a range of final states are observed in an experiment it is possible to tell if they were formed in direct excitation from the ground state or whether excitation also proceeded through an intermediate state.
A: A given state has one single wave-function. Thus, the information about the different preparation types is not encapsulated in that wave-function. 
But keep in mind that each preparation type has its additional products. For instance if the excited state you obtained came from an even higher excited state, a photon was emitted and its wavelength can tell you which was the higher level.
But the final excited state that you obtained, cannot tell.
Good luck  
