Re: IONS in metals

["Bob Sciamanda" <trebor@velocity.net>]

Hi Ludwig,

Even within classical mechanics the force concept can be subsumed within
the use of a Lagrangian or Hamiltonian function.  True, the force concept
told us how to construct these functions, but they can then be used as
the basis of speculations based on variations of these functions -
possibly resulting in new systems and behaviors not intuitively amenable
to simply an inter-particle "force" description (fields might then be
endowed with particle properties, to "save" the model).

Simple example (not a speculation) : within classical theory, two
interacting charged particles will not in general conserve momentum and
energy (between themselves) and their motions will not exactly follow the
dictates of a two-particle "Lorentz" force - hence we invent some
"particle properties" for the fields (ie; we read them into the
Lagrangian/Hamiltonian which works!).  I don't think that it is possible
to exactly describe the (classically predicted) motion of two electrons
shot past each other in terms only of forces between the two particles
(even if you want to dream up forces of the  particles on the fields!).
The fields carry momentum and energy, but they are not "acceleratable
masses";  F=ma does not apply, even in concept.

We are now so used to including these fields (first introduced as purely
mathematical entities) as "quasi-substantive" participants that we miss
the stretching effect which these notions had on the original Newtonian
force concept and the selective particle properties which it slyly
attaches to the fields (presaging the photon?).

The quantum mechanical particle state (and its time development) is a
completely different conceptual and physical entity.  You are correct in
asserting that in the Shroedinger representation the potential energy
V(r) enters into the Hamiltonian.  It contributes to the specification of
the eigenstates of energy available to the particle.  At this point,
there emerges the existence of impossible particle states, and this is
not attributable to any new Newtonian force in any simple intuitive
sense.  The force concept has really been subsumed and will re-emerge
only if one goes to a situation where a classical limit applies, and
considers the behavior of the average values of observables (Ehrenfest's
equations).

I don't think the answer to your pedagogical problem lies in seeking a
Newtonian type force to account for these phenomena of "particle
trapping"; there isn't any.  More important  is the Pauli principle and
the "quantization of states" dictated by boundary conditions; classically
possible states may be forbidden.  An electric force field applied to an
insulator will not accelerate an electron because there is no unoccupied,
appropriate state available to it, etc.

I think that you need to sell your students the denial of classical force
effects which Bohr asserted in 1913.  Tell them about the Bohr atom, its
restricted set of orbits and the impossibility of classically permissible
motion out of an orbit until enough energy is available to get to an
unoccupied (bring in Pauli too) orbit.  Just the notion that quantum
mechanics often denies the availability of a continuum of states and can
then "trap" a particle in a state without a definable "trapping force"
should  allow them to model a lot - still thinking in terms of forces.

Sorry I rambled - it's your fault!

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>
To: phys-L@atlantis.uwf.edu <phys-L@atlantis.uwf.edu>
Date: Sunday, October 04, 1998 9:20 AM
Subject: 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