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Re: IONS in metals



Bob Sciamanda wrote:

Forces are human inventions which help us model our
observations. However, quantum mechanical models are
not always simply understandable in terms of this concept.

As far as I remember, the central concept of QM is potential, V.
We must specify a potential function to write down the
Schroedinger equations for specific problems, for example,
Coulomb's potential in the case of the single hydrogen atom.
What prevents me from using F=-grad(V) and to think that
there is a force behind any smooth potential function?

The concept of F remains central in QM. I tell students that
QM is an extenuation of classical physics, just like relativistic
kinematics is an extenuation of classical kinematics. Quantum
granularity does exist for ordinary macroscopic objects but
the steps are so small that for all practical purposes we can
say that all energies are allowed. What is wrong with this?

At the end of the message Bob writes:

(As a pedagogical crutch, you might introduce the "exchange
force" to help in some cases where the Pauli exclusion
principle is the controlling factor under discussion.)

Keep in mind that my hypothetical student (see below) was
in an introductory physics course. He would only be confused
if I follow your suggestion. I do not like "borrowing from the
future" why EXPLAINING things. Let me propose an
alternative. Here is the situation to which Bob is referring:

How to deal with this hypothetical situation? It is a
pedagogical issue. I have no problem in pretending that
Galilean kinematics is exact, but I will now face a problem
of pretending that electrostatics I teach is logically
consistent with mechanics. Galilean kinematics is at least
approximately correct in common situations. Something
is missing in our ways of introducing e&m. What is it?

In other words, what is the nature of the "glue" binding
excess electrons to the surface of a metallic object? Let me
improvise the answer by using an analogy. Consider
static friction. We pull an object and it does not move. We
pull stronger and it still does not move. But eventually
"the glue" can not hold it.

Some kind of binding force must exist to keep electrons on
the surface. We can give it a name, for example, metallic
surface force, but this is only the first step. A good question
for future investigations. I have no idea what the nature of
this force is; I just invented it to solve our dilemma. To the
best of my knowledge, I would say, this force has not been
studied in detail.

Free charges do escape from metallic surfaces when their
concentration becomes excessive (as discovered by Franklin).
This shows the analogy between the metallic surface force
and the static friction force. Both grow, up to some limit,
and than .... The electrostatic surface tension force (another
possible name) grows with concentration of surface charges.
Is this an acceptable presentation for first physics course ?

Ludwik Kowalski