jshrager
Gold Member
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Why is it:
$$ \langle A \rangle = \int dV ~ \psi^* (\hat{A} \psi) $$
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.
$$ \langle A \rangle = \int dV ~ \psi^* (\hat{A} \psi) $$
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.