I'm new to the theory, but I think the reason is that spectrum of operator is defined for bounded operators. There exists also some extended definition of spectrum for unbounded operators, but it can be empty (unlike the spectrum of a bounded operator).
BUT I read that in quantum mechanics every...
Hi, I'd like to know if the following statement is true:
Let \hat{A}, \hat{B} be operators for any two observables A, B. Then \langle \hat{A} \rangle_{\psi} = \langle \hat{B} \rangle_{\psi} \forall \psi implies \hat{A} = \hat{B} .
Here, \langle \hat{A} \rangle_{\psi} =...