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Re: [Phys-l] "filling" the space in an atom




Bob Sciamanda wrote:

"If you use a very weak beam, so that only one particle goes through the
system at a time, you do indeed get the BUILDUP of a diffraction pattern,
consisting of many "point" hits. That is because we are measuring each
particle's final position on the screen. An individual particle does not
then produce the entire diffraction pattern."


This is precisely what I meant - a fainted beam with one particle at
a time - the way this kind of experiemnt is accurately carried out nowadays.
And if in each such passing, a particle went through only one slit, then the
collective result of many landings after a long exposure would produce a
Gaussian bump on the second screen with the top against the midpoint
between the slits. It WOULD NOT produce the observed diffraction pattern.
The same is true for light interference in a Michelson or Mach-Zender
interferometer with a dimmed beam containing only one photon at a time -
each such photon interferes with itself after superposed motion in both
arms of the interferometer at once.
(See, e.g., P. Dirac, Principles of Quantum Mechanics).

Moses Fayngold,
NJIT

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Fayngold, Moses" <fayngold@ADM.NJIT.EDU>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, October 26, 2006 3:05 PM
Subject: Re: [Phys-l] "filling" the space in an atom


On 10/25/06 John Denker wrote:

"As to delocalization in particular, if you ask whether the electron
in a hydrogen atom is "a little bit here" *and* "a little bit there"
at any particular time, the answer is absolutely no.
This is an entirely nontrivial result, because it is directly
connected to the electrostatic self-energy. One part of the
"electron cloud" does not repel other parts. It's the same
electron after all, and it cannot repel itself."


I do not think this is a valid argument. That an electron in a
stationary state within an atom can be described as "smeared out"
over atomic space, does not imply the emergence of self-interaction.
I would say, it you bring in self-interaction for one configuration,
it will stay in all of them including the state described by an
eigenfunction of the position operator (infinitely sharply localized)
(See, e.g. Feynman's Lectures on Phys.)
Reversing the argument, - we know that the magnetic moments of the
1-electron quantum orbital states within an atom can be calculated as
the result of continuously distributed current (figuratively, spinning
of the electron probability cloud filling out the atomic space).
In this case the picture of the electron filling the atom gives exact
results (See, e.g., D. Blokhintsev, Quantum Mechanics).

"Also, if you pick any particular small region within the atom, and
ask whether the electron is in that region, the answer is very,
very likely to be no. If there are N such regions, N-1 of them
will be empty at any given time."

I absolutely disagree with this. If this were true, the electron
in a diffraction experiment would pass either one slit, or the other
with the result that we would not have any diffraction pattern at all.
Any claim that at any given time the electron occupies only one spot
leaving the others free is referral to hidden parameters, which were
shown to contadict the experiemnts (See, e.g., J. Bell,
Speakable and unspeakable in QM, and A. Aspect's experiements)

In another poster John says, that if we prepare an electron in a
localized state, we will find it later in this state. This is only
true in a special case when this state is stationary, that is we have
taken special care to put the electron in an appropriate very deep and
narrow potential well. Otherwise, the electron state will spread the
faster, the narrower its initial wave packet (in non-relativistic QM
- infintely fast for infinitely narrow initial state).


Moses Fayngold,
NJIT

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Forum for Physics Educators
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