Finished a research paper and feel horrible now We've all heard of postpartum depression, though I'm not a woman so I have no idea what it's really like. 

I am wondering if there is any medical/psychological evidence to support similar (reported) feelings after the completion of a big research project.  

This is my (I'm the sole author each time) fourth time sending a paper to a journal after spending countless hours working to finalize the draft. 
 This typically involves a frenzy at the end where I work 12 hours a day trying to perfect the paper. This is in addition to the stress incurred while actually creating the research  (in my case, mathematics) in the first place.  

Each time I finish a paper, including my most recent, I have feelings of emptiness  and anxiety.  I'm not here for medical advice, I'd just like to know if anyone is aware of some scientific basis for these emotions.
I don't have a name for it, or a scientific basis, but I experienced exactly what you are describing: a general numbness/boredom that lasted a couple of weeks after seeing a paper published - everything was pretty hectic up until that point.

My guess is that this is due to something called 'lifestyle changes' (also a hypothesised contributor to postpartum depressions) - your life changes almost instantaneously upon submitting a paper. Before that you were totally hyped up, working really long days, getting by on the fear that things wouldn't work out and the adrenaline when it turned out they would after all. And then when you're done you are exhausted and all your previous drivers (that all related to getting your research project done) are gone. You have to recuperate and you have to find something new to live for (next project? family? a little bit of Mozart maybe?).

Good luck!