I noticed that this problem was marked "off-topic". I've looked at many other questions about being "off-topic" but haven't gotten a satisfactory answer from any of them, which is why I chose to ask this. Yes, OP says that it is a physics question, but (s)he also says that it requires math. And as far as I can tell, the problem doesn't need physics and is purely mathematical. I'm not sure if that was the right protocol. If it was, then can we improve the question to make it fit the category? If not, can we reverse it?