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I've read in a couple of different places, and was told when first learning about quantum mechanics, that Schroedinger interpreted the wavefunction as being representative of the charge distribution of the electrons in a system. This idea was later replaced by Max Born's interpretation of the wavefunction as the probability density of the electrons in a system which is the common view now.

It's quite apparent that quantum mechanics is built on this idea of probabilistic interpretations, and so without it QM would have problems. It's not obvious to me, however, how one makes the jump from interpreting the wavefunction as a charge density to a probability density. Or maybe a better question to ask is this: why did Schroedinger interpret the wavefunction as a charge density? Specifically, what physical motivation is there for this interpretation? Furthermore, in what situations does this interpretation fail? I could imagine some problems with Pauli Exclusion, but perhaps not. In that case, one would still give as an axiom that the wavefunctions of fermions are anti-symmetric upon particle exchange and then one would have that there could be no charge density in that region of space, and everything might still be fine...

So, to narrow things, in what situations does the interpretation of the wavefunction as a charge density fail?

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  • $\begingroup$ Could you quote the mentioned "couple of different places"? I simply don't believe that Schrödinger interpreted $|\Psi|^2$ as the charge density. I mean, it is quite apparent from the very Schrödinger's work that, in general, for a many-variable wavefunction $\Psi$, $|\Psi|^2$ could not be the charge density. Such interpretation will work only for $\Psi$ that describes a single charged particle. $\endgroup$ – Wildcat Aug 10 '16 at 8:50
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    $\begingroup$ Found this similar question on Physics.SE, the first answer to which expresses the same concern. $\endgroup$ – Wildcat Aug 10 '16 at 8:54
  • $\begingroup$ I'll provide links later but at the very least there's a Wikipedia page on interpretations of quantum mechanics which says this under the history section. I've heard it a number of times by word of mouth and there's even a simple dimensional argument which refutes that interpretation. It seems Schrödinger later changed his interpretation of the wavefunction, but if you know of a paper when he did this I'd be interested to read that. $\endgroup$ – jheindel Aug 10 '16 at 17:53

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