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$$ \langle A \rangle = \int dV ~ \psi^* (\hat{A} \psi) $$

As opposed to:

$$ \langle A \rangle = \int dV ~ (\hat{A} \psi^*) (\hat{A} \psi) $$

The op can substantially change the wf, so it would seem to make more mathematical sense (at least from a linear algebra pov) to operate on both the wf and its mod, otherwise, as we do it now (first expr) you're getting a very odd product. Is this is a property of the way that wfs are formulated? Are they a special case where this isn't required? Or maybe it's a magical property of hermetian operators? Or maybe it just works and I shouldn't think too hard about it.

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# Shouldn't the operator be applied to both the wf anD its modulus?

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