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*From*: Bruce Sherwood <Bruce_Sherwood@ncsu.edu>*Date*: Thu, 14 Nov 2013 15:44:50 -0700

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 toeE,

the force acting on the proton due to the applied field E, which is F =

so (ke/R^3)r = E, and the displacement of the proton is proportional tothe

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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**Follow-Ups**:**Re: [Phys-L] Energy & Bonds***From:*Bernard Cleyet <bernard@cleyet.org>

**References**:**Re: [Phys-L] Energy & Bonds***From:*George Przywolnik <George.Przywolnik@scsa.wa.edu.au>

**Re: [Phys-L] Energy & Bonds***From:*Paul Lulai <plulai@stanthony.k12.mn.us>

**Re: [Phys-L] Energy & Bonds***From:*Bill Nettles <bnettles@uu.edu>

**Re: [Phys-L] Energy & Bonds***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] Energy & Bonds***From:*Bernard Cleyet <bernard@cleyet.org>

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