Re: Does element mass = # of electron + neucleons??

On May 30, 9:27 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
Jeckyl wrote:
Yes .. but does an electron actually 'move'.

As is often the case, you need to be more precise, here in defining what
you mean by "move". For instance, one might imagine that the electron in
an hydrogen atom "moves" in the following sense: If one measures its
position at time t0, and again at time t1, being careful to not disturb
the atom as a whole, one obtains different positions (except possibly
for rare cases when it happened to come back). This fails because to
measure the position accurately enough to localize it inside the atomic
size requires so much energy that the atom is ionized and cannot remain
an atom.

Here's an attempt to define "move" classically: as the electron is both
charged and bound in the atom, if the electron "moves" then it must be
accelerated and thus radiate electromagnetic waves. None are observed,
so the electron does not "move".

For further discussion I must use nonrelativistic quantum mechanics,
using the ground state of the electron in the hydrogen atom. I'll assume
the nucleus of the atom remains fixed in space (unrealistic to be sure,
but it greatly simplifies the discussion and is faithful to what was asked).

Perhaps this meaning will do: the electron "moves" if the expectation
value of its position changes with time. For this meaning the electron
does not "move".

Perhaps this meaning will do: the electron "moves" if it has nonzero
expectation value of 3-momentum in some direction. For this meaning the
electron does not "move" (contrary to what others have said -- simple
proof: the ground state is spherically symmetric, so there is no
direction in which the expectation value of the 3-momentum could point,
hence it must be zero).

I don't think this is acceptable. A classical harmonic oscillator has
a zero expectation value of 3-momentum, but this does not imply that
the oscillator is at rest.


Perhaps this meaning will do: the electron "moves" if it has nonzero
expectation value of orbital angular momentum. For this meaning the
electron would not "move" if it is any S state, but would move if it is
in any other bound state. As the ground state is S, the electron does
not "move".

... I'm sure that other possible meanings of "move" could be found, but
I think this gives the basic idea: I know of no meaning of "move" that
applies to the electron of a hydrogen atom (in its ground state,
relative to the nucleus).

Got a problem with expectation value of kinetic energy?

Note also that had you asked instead "does the
electron spin?", the answer would be unambiguously in the affirmative.
So I leave it to you to figure out how an electron can "spin" without
"moving"....

Tom Roberts


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Relevant Pages

  • Re: Does element mass = # of electron + neucleons??
    ... For instance, one might imagine that the electron in an hydrogen atom "moves" in the following sense: If one measures its position at time t0, and again at time t1, being careful to not disturb the atom as a whole, one obtains different positions. ... Perhaps this meaning will do: the electron "moves" if the expectation value of its position changes with time. ... For this meaning the electron does not "move" (contrary to what others have said -- simple proof: the ground state is spherically symmetric, so there is no direction in which the expectation value of the 3-momentum could point, hence it must be zero). ...
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