For all the hullabaloo I've read in popular science books and the strong emphasis my physical chemistry text book places on the differences between classical and quantum mechanics, half-way through the semester I'm sitting here saying to myself: It ain't that weird. I half-way wonder if the only reason it seemed weird initially was because everyone told me how friggen' weird quantum mechanics are. Sure, an electron doesn't behave like a baseball. Is there really any reason why we think that it should? Even in Physics 1, whenever dealing with real objects we would make it clear that we were inventing a point that made all the classical laws apply (Center of Mass), but that this point wasn't a real point, so that if the object were destroyed mid-flight, the center of mass would still continue due to inertia. And, actually, the originators of quantum mechanics knew that it would be absurd to propose a physical system that entirely violated what had already been observed, so they built equations around the idea that as you took the limit of them that you would get classical results. So what gives? Why does every voodoo mystic and half-baked spiritualist in the world think the deep secret of the universe lies in quantum mechanics? I certainly acknowledge that I'm going at this at the depth of Chemistry, and not at the depth of physics (half way through and we've just started spectroscopy. I'm told that physicists tend to finish their first semester of quantum with solving the hydrogen atom), but all the quantum "Weirdness" is still there.
Really, the quantum concept can be introduced utilizing series and sequences. And seeing as we don't exactly live at the size of electrons and can only interpret spectroscopic data to make inferences about what's going on, it makes perfect sense that the wave equation is an abstract description of what's going on, and we need observable values that we in the macroscopic world actually can see. In fact, it almost makes MORE sense than trying to plot out the trajectory of electrons and protons, because we can't actually see these things, and testing what we can see is exactly what science is all about.
Maybe it's the shift from determinism to the "probabilism" (no, not a real word) that really gets people, but half-way through, and fully realizing that quantum mechanics aren't yet entirely complete... I seriously enjoy learning about and thinking about them, but I'm just not quite grasping what's so weird about them. Difficult? Certainly. Abstract? Yes. But the same held (and still holds) true in my classes on chemistry, physics, and mathematics.
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