would anyone mind showing me, for example, how to prove that d^2/dx^2 is a hermitian operator? i've tried to work it out from two different books; they both prove that the momentum operator is hermitian, but when i try to apply the same thing to the operator d^2/dx^2 i get lost pretty quick. thanks in advance. also, does anyone know a book on QM written from a not so mathematical perspective? right now i don't really care for rigorous mathematical proof, i just want to know how to do things and why i am doing them. all this stuff about operators seems very arbitrary (i know that its not, but thats how it appears with my current level of understanding). right now my QM course just seems like i'm learning random mathematical proofs. like someone trying to learn newtonian mechanics without knowing what a body is.