My question is about both sides of the same coin. First, does a hermitian operator always represent a measurable quantity? Meaning, (or conversely) could you cook up an operator which was hermitian but had no physical significance? Second, are all observables always represented by a hermitian operator? e.g. (again, conversely) does there exist some operator which is not hermitian but has real eigenvalues and therefore(?) represent an observable? It's my first day back in school and I pulled an all nighter last night so forgive me if I have had any (possibly serious) brain farts.