>>8538736But that's not even difficult.
We DON'T use the integral in quantum; not for anything that's quantized, at least. Literally the first quantum mechanics was defined by the use of non-integrals (Rayleigh and Jeans fucked this up and used the integral, and got the wrong answer, Planck said "no integrals" and got the right answer).
The second part, while valid, doesn't violate anything; again, nobody is assuming that's continuous. It violates nothing. This is 2nd year stuff.
I hope you guys aren't ACTUALLY all just freshmen in engineering... Right?