Re: QUANTA

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

At 09:12 AM 3/7/99 -0500, David Abineri wrote:
> Does one look any differently at an EM wave generated by the falling of
> an electron from one energy level to another OR the EM wave generated in
> a radio antenna which, as I understand it, is generated by a continuous
> oscillation of electrons in the antenna?

I don't.

> Does the notion of a quantum of energy apply in both cases? If so, how
> does one think of it in the latter case?

I would say the notion of "quantum of energy" applies in *neither* case.
Energy is not quantized.  Look at the rainbow:  you can have any energy you
want.

Consider a high-Q LC circuit connected to a small antenna.  Because of the
high Q, it will radiate at a more-or-less definite frequency.  The emitted
photons will have a correspondingly more-or-less definite energy.  There's
nothing mysterious about it.

The sharp spectral lines we see in atomic physics depend on three things:
  1) Atoms are really small.  They are too small to couple well to the
Maxwell field.  Therefore they are always high-Q oscillators.  A Q of 10^8
is typical.  (The same cannot be said for dye molecules, which are large
enough to couple rather better.)
  2) Angular momentum *is* quantized.  The angular momentum of a typical
atomic state is not just a half-integer, it is a *small* half-integer.
  3) Atomic frequencies are high compared to kT/h (remember k/h is 20GHz
per Kelvin).  Therefore it is relatively easy to prepare atoms in
particular states.  In contrast, radio-frequency oscillators are typically
in a thermal mixture of states.

Combining these facts (which have everything to do with atoms and almost
nothing to do with energy itself) we can see why the width of spectral
lines is small compared to the separation between them.

Other than that, atoms are just little antennas.

Cheers --- jsd