It's already been said, but here's my bit. I was a 911-dispatcher for nine years. Generally, schizophrenics are not dangerous HOWEVER, that said, they can get into quite a bit of trouble if they're off their meds, and there are exceptions--those who act on the delusions.
So the advice to bring this to the attention of both your apt manager and the local police is very good advice. Tell them that you know there probably isn't much that they can do, but you'd like them to be aware of the situation in case it escalates.
I am against buying a gun for a myriad of reasons, but the biggest one is that in my experience, people who are not proficient in firearms and try to use them in a life-threatening situation are more likely to (a) accidentally shoot themselves or a family member or (b) have the weapon taken from them and used against them. If you're willing to invest the time in the training it takes to become proficient, go right ahead--but also be aware that if you have a child in the house, you are taking a huge risk. Unless of course you lock the weapon up--in which case it will be difficult to reach in an emergency.
Jankyn, wishing you the best