- #1
hitche
- 3
- 0
Hi, I'd like to know if the following statement is true:
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!
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!