hitche
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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} = \int_\mathbb{R^3} d^3x \psi^* \hat{A} \psi is standard definition of expectation value of an operator \hat{A}.
If this doesn't hold, could you provide any counterexample? Thank you!
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} = \int_\mathbb{R^3} d^3x \psi^* \hat{A} \psi is standard definition of expectation value of an operator \hat{A}.
If this doesn't hold, could you provide any counterexample? Thank you!