https://physics.stackexchange.com/q/149004/ was put on hold as too broad, but edited the same day. Now it's been on hold for a few days. Is it still too broad?
Questions that are edited after they are closed enter the reopen queue. There has not been a single reopen queue cast on that question, indicating that the reviewers still thought it too broad.
My personal view is that this is a mixture between too broad, unclear what you're asking and non-mainstream:
You just throw the matrix exponential in there and essentially ask "Is this a wavefunction?". I bet one can write down something looking like a wave equation to which that exponential would be the solution, but what do you mean by "[...]is there a natural way to extend the previous wavefunction interpretation[...]"? What was the previous wavefunction interpretation? (Just writing down an exponential doesn't make it a "wavefunction"!) Why would you expect the matrix exponential to have the same interpretation? What system are you trying to model? It's really not a very focused question.