Hi, I'd like to know if the following statement is true:(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex] \hat{A}, \hat{B} [/itex] be operators for any two observables [itex]A, B[/itex]. Then [itex] \langle \hat{A} \rangle_{\psi} = \langle \hat{B} \rangle_{\psi} \forall \psi [/itex] implies [itex] \hat{A} = \hat{B} [/itex].

Here, [itex] \langle \hat{A} \rangle_{\psi} = \int_\mathbb{R^3} d^3x \psi^* \hat{A} \psi [/itex] is standard definition of expectation value of an operator [itex]\hat{A}[/itex].

If this doesn't hold, could you provide any counterexample? Thank you!

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# Expectation values equality

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