Low Dimensional Physics

There is something stupidly mysterious about solid state physics. I have never fully understood the basis for most of what it includes, but its not like I've never tried. There's a general absence of knowledge, at least the reasoning to behind most of the alleged facts. No one seems to know how things arrive the way they are. My low-dimensional prof. (snort) happens to be an embodiment of the same, but I don't think he's to blame for the two steps that the research level derivations he conveniently writes on the board, expects us to remember and write them out in the exam in exactly the same form as he has done, take, but apparently there's no other way anyway. The learning aspect of the course lies largely on interpretations of the various curves that get plotted as a result of formulae/functions that appear out nowhere but are somehow related to either of a) potential wells, b) excitons, c) {insert random nanotech/quantum buzzword here}, and as a result of the interpretations add another fact to the list of facts that hold little importance even though its like the biggest thing going around here.
That's also my grudge against quantum mechanics. The equations never simplify. For every new statement you add 5 more unknowns. Its an equivalent of the Drake's equation for me, but for some strange reason works great. The only way to arrive at any sort of solution, which, mind you, is almost always qualitative, is to take hints from other walks of life and physics, and consequently make enough approximations to reduce the 21 thousand variable model to something that is linear and hence a chid's play. Everyone in solid state has got more publications than those exist playing around with this. This comes surprisingly close to device physics. Ouch.