I was going to respond until this caught my eye. In ODEs there is Picard's existence and uniqueness principle. It means that if a solution or set of solutions exists to an ODE then not only does the solution(s) but it is the only set(s) of solutions.
Make of that what you will, but I wanted to add Picard's theorem and comment that QM explanations as most see them are just interpretations and it's important remember that interpretations of math is all it is. It's hard to create interpretations of math that is a consequence of phenomena that is so fundamentally weird which leads to a lot of confusion.
What I'm trying to say is that even after 2 classes on QM I have not much of a greater fundamental understand(at least I feel this way) than the laymen conceptual explanations. What it did do for me is show that these explanations stem from the math, and unless you have a PHD in this stuff and you've been doing it for years the true insight is hard to gain. Even then, I have doubts. The math exists and can be done, but the interpretations of it that we actuallu talk about can be much less clear and difficult to understand.
With that said, my interests lay with rockets and not QM, so the time I spent "solving"(I say that with apprehension since the basics have been solved for nearly a century now) these equations were frustrating boring and more something to just get it over with. It's all approximations and computer simulations these days so there's not much to do except how to manually solve these suckers and that's what QM really is. At least to me, when I think of it I don't think of as spooky action at a distance or any other of the weird repercussions, but the transmission or reflectration rates of your particle. It's just really annoying diffeq and stats that rivals E&M in how frustrating it is to solve.
I'm not really sure what this response was supposed to mean or say but there it is. That math sucked and to assign a real world interpretation to it seems ridiculously difficult even after having done that basic century old math and seeing how hard it is to create an explanation from the result first hand.