Re: [Phys-L] Energy & Bonds

[Bruce Sherwood <Bruce_Sherwood@ncsu.edu>]

For me, it's weird that so often (as is the case in the wolfram.com demo
discussion) one simply starts with putting the electron on a damped spring,
which sounds totally nuts. The model needs some justification.

In Feynman I 31-4, in the chapter on the origin of the refractive index, he
says about modeling the binding of the electron to the atom with a
spring-like force, "You may think that this is a funny model of an atom if
you have heard about electrons whirling around in orbits. But that is just
an oversimplified picture. The correct picture of an atom, which is given
by the theory of wave mechanics, says that so far as problems involving
light are concerned, the electrons behave as though they were held by
springs".

Then in Feynman II 32-2, in the chapter on the refractive index of dense
materials, he says, recalling the earlier discussion, "We emphasized that
this was not a legitimate classical model of an atom, but we will show
later that the correct quantum mechanical theory gives results equivalent
to this model (in simple cases)."

On the other hand, I showed that a semiclassical picture provides a
reasonable justification for the harmonic oscillator model. I can't now
identify it, but I think I've heard of a theorem by Feynman that once
you've used quantum mechanics to get the charge distribution, you can then
do classical E&M with that charge distribution. In the model of the
hydrogen atom I discussed, the (crudely) uniform-density sphere of electron
charge comes from quantum mechanics, after which it's legitimate to do
simple classical E&M to see that the induced dipole moment is proportional
to the applied electric field.

Bruce


On Thu, Nov 14, 2013 at 2:59 PM, Bernard Cleyet <bernard@cleyet.org> wrote:

> On 2013, Nov 14, , at 12:59, John Denker <jsd@av8n.com> wrote:
>
> > Note that for molecules (including macromolecules,
> > including chunks of solid) /at equilibrium/ near the
> > bottom of the energy-level diagram, the interatomic
> > force -- including KE as well as PE -- can be modeled
> > as a spring /to first order/ for small oscilations.
> > This is not suprising; almost anything is linear to
> > first order!  For large-amplitude oscillations, this
> > pseudo-spring becomes exceedingly nonlinear.
>
>
> On 2013, Nov 14, , at 10:37, Bruce Sherwood <Bruce_Sherwood@ncsu.edu>
> wrote:
>
> >  In equilibrium this force is equal to
> > the force acting on the proton due to the applied field E, which is F =
> eE,
> > so (ke/R^3)r = E, and the displacement of the proton is proportional to
> the
> > applied field, which means that you can model the response to an applied
> > field with a spring-like force.
>
>
> Hence the Drude-Lorenz approximation.
>
>
> http://demonstrations.wolfram.com/DrudeLorentzModelForDispersionInDielectrics/
>
> This works for artificial dielectrics at X-band to model optical
> dielectrics.
>
> Strong's Concepts of classical optics does this with pics. of springs and
> balls.
>
> bc
>
> p.s. for some time I've thought of modeling anomalous dispersion using a
> multiple wire dielectric.  Bell Labs did this, but insufficient detail
> reported.  Anyone out there done this?
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