Re: dielectric constant

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
> How are damping coefficients of atomic levels calculated?
> Are they used as adjustable parameters [to match the
> experimental n(w) function]

Yes, if you want.

> or are they calculated independently?

Yes, if you want.

> I am referring to the formula 31.20,
> on page 31-8 of Faynman, vol II. In my mind they
> are "frictional" coefficients of some kind.

It is possible (but not necessary) to take them as
phenomenological adjustable parameters.

It is also possible to calculate them _ab initio_.
In the isolated atom (e.g. in a dilute gas) it's
just radiation damping.
 -- You can get an order-of-magnitude estimate for
this damping using classical electrodynamics:  The
electron is a charged particle that radiates when
it undergoes acceleration (e.g. when it runs around
in an atomic orbital).  See _FLoP_ (_The Feynman Lectures
on Physics_) equation 32.2 for
 -- Obviously the classical expression is going to fail
miserably for electrons in the atomic ground state,
which (in some cases) are accelerating but (by definition
of ground state) are not radiating (according to the
usual conception of radiating).  So we have to use
the quantum description:  time-dependent perturbation
theory.  Fermi's Golden Rule.  This explicitly accounts
for what state you're radiating from, what state(s)
you're radiating to, and the strength of the coupling
(e.g. charge which couples to the EM field).  This is
not covered in intro QM courses, but in the course after
that.

Sources for this include:

S. Gasiorowicz _Quantum Physics_ -- Decent, relatively
introductory.

Gordon Baym _Lectures on Quantum Mechanics_ -- Classic.
Beware some end-of-chapter problems are fiendishly hard.

J.J. Sakurai _Modern Quantum Mechanics_ -- I'm not
familiar, can't comment.

Kurt Gottfried _Quantum Physics_ -- Thorough and sensible, but
not always gentle.  Slight tendency to use "standard" notation
without introducing it, forgetting that student's weren't born
knowing the notation.

Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe _Quantum
Mechanics_ -- Huge books, detailed, modern approach.

Laudau & Lifshitz _Quantum Mechanics (Non-Relativistic Theory)_
Stay away.  Old-fashioned.  Infamous for "proof by pun", that
is, "deriving" a well-known valid result by throwing around a
bunch of formulas starting from an invalid starting point and
proceeding by invalid logical steps.  Or perhaps more commonly,
using valid but irrelevant starting point and intermediate
steps, such as:
 -- roses are red
 -- violets are blue
 -- conclusion, QED.