Most fields within the physics realm use mathematics to explain phenomena that can be observed. It's as if reality is "one step ahead" of mathematics, in that in most cases an event is observed, then explained. The astute reader may point out that Newton's F = ma cannot be derived and thus flies in the face of everything I just said, but that is beside the point, and it totally destroys my argument. Therefore, to said reader I say, "Shut up."
Quantum mechanics starts with an underivable equation (my beloved Schrödinger equation), as does classical physics, but many of the mathematical predictions that can be made from it make no intuitive sense whatsoever. For example, what do you think happens when you throw a ball at a solid wall? It bounces back. What do you think would happen if you threw that ball at that wall a billion times? It would bounce back a billion times. Makes sense, right? Wrong. Quantum mechanics says that the wave function of the ball will still propagate through the wall, albeit in a much diminished form. In other words, QM says that each time you throw that ball at that wall, there is a chance it will fly straight through it. It's not because the ball will break through the wall so much as it will simply go through it as if it were not even there. I've read crap like this in books that describe some of the qualitative results of quantum mechanics, but now I've proved it mathematically, and it's making my brain hurt.
I'm just not used to being such a captive to pure mathematics. In general physics it was relatively easy to ballpark the outcome of an event because often times I've witnessed such an event myself. If you put two magnets close together, they tug on each other a whole lot harder than they do when they're far apart. Duh. So when I do physics problems involving magnets moving toward or away from one another, I can look at my answer and ask myself, "Does this make sense?"
With QM I can't do that anymore. When a problem asks me, "What happens when a particle encounters this barrier?" I'm tempted to say, "It bounces back," but then I remember I'm studying QM and I revise my answer slightly to, "I have no freaking clue." I just have to do the math, and even if it looks like the stupidest answer on the face of the earth, I have no benchmark by which to judge it. I can't say, "That doesn't make sense," because none of QM makes sense. Even though Erwin Schrödinger created that equation, he himself had no idea what it actually described. It wasn't even he who figured out what the wave function meant - Max Born did.
I'm not frustrated by QM, I'm just too fascinated by it to be productive with it.
