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the probability of finding particle is a constant with time <ψ|[itex]\partialψ[/itex]/[itex]\partial(t)[/itex]> = -<[itex]\partialψ[/itex]/[itex]\partial(t)[/itex]|ψ> , the equation holds for all ψ so the time derivative operator is an anti-hermitian operator, but then consider any hermitian operator A, the rate of change of A is d(<ψ|Aψ>)/dt = <[itex]\partialψ[/itex]/[itex]\partial(t)[/itex]|Aψ>+<ψ|[itex]\partial(Aψ)[/itex]/[itex]\partial(t)[/itex]> , interchange the anti hermitian operator for the first one the equation equals to 0 which means every observable is conserved in all situation and it's clearly wrong, so where did I think wrong? Please show me

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