> but the result will have a lot of functions that are not differentiable and, thus, not quantum mechanics wave functions. So, I would be reluctant to take the

> but the result will have a lot of functions that are not differentiable and, thus, not quantum mechanics wave functions. So, I would be reluctant to take the resulting actual Hilbert space as what physics was talking about. Wavefunctions aren't differentiable functions, because they're not functions. They're distributions - described in general by the rigged Hilbert space structure I described previously, and in the simplified normalizable case typical of introductory courses by L^2(R^n). > to try to understand what is known and maybe to try to clean up what is commonly called its many loose ends and maybe make progress in some applications, e.g., condensed matter physics, super conductivity, maybe even something as common as just why a grid of wire reflects radar waves, maybe connecting with gravity, dark energy, the first second, the Casimir effect, Hawking radiation, and I would include entanglement, then IMHO we need to be as clear as possible on the definitions, theorems, proofs, passing between physics and pure math, etc. Ok, but that's not what undergraduate textbooks are for. If you want mathematical physics without any pedagogical concessions, go read mathematical physics papers.