Re: nonlocalized electron's EM field

From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 09/22/04 

Date: Wed, 22 Sep 2004 08:45:51 +0000 (UTC)

Blake Winter wrote:

> Recently I heard that there was an experiment done in which an
> electron was placed in a two dimsionional "ring" of sorts, in such a
> manner that its wavefunction spread throughout the ring but was
> essentially still localized in the perpendicular dimension. Then the
> electric field resulting was measured and was found to behave as
> though there was a charge distribution proportional to the probability
> density from the wave function with a total charge equal to that of an
> electron.

I don't know about the experiment, but the outcome is exactly how it
should be, from a QFT point of view. Indeed, the charge density of an
arbitrary Fock state is the expectation
    e(x) = <Psi_0(x)^* e Psi_0(x)>,
where Psi_0(x) is the time component of the Fermion field. For a
single electron in the pure state psi we simply get e(x)=e|psi(x)|^2.
This is also the chemists' point of view; see the section
'How real is the wave function?' in my theoretical physics FAQ at
    http://www.mat.univie.ac.at/~neum/physics-faq.txt

> Unfortunately the person who told me about this couldn't remember who
> had done this experiment or where to find anything more about it,
> except that it was probably in "Schrodinger's Kittens". Can anyone
> point me to more information about it? Maybe even the original paper?

I'd be interested in the details, too.

> Also, has it had any profound influence on our understanding of
> quantum theory?

Maybe it will lead to more attention for the fact that what we can really
measure are all sorts of expectations, and not just eigenvalues
(which are simply expectations in an eigenstate). Cf. my paper
quant-ph/0303047 = Int. J. Mod. Phys. B 17 (2003), 2937-2980.

Arnold Neumaier

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