From: terry@asl.dl.nec.com
Subject: Re: A Good Question
Originator: terry@aslss01
Organization: (Speaking only for myself)
Date: Tue, 5 Jan 1993 02:04:30 GMT

Hi folks,

In article <C0CK8o.J4H@efi.com> chrisp@efi.com (Chris Phoenix) writes:

> ... a farfetch: [1] Electrons, like everything else, have a wavelength.
> [2] A palladium-water interface or crystal boundary might be a pretty
> good reflecter of electrons...

Yes on both counts.  They have wavelengths, and a metal crystal that has
an insulator at its surface provides an extremely efficient "mirror" of
such wave-like electrons.  In fact, you've just described the fundamental
principles of how electrons motion in a metalic crystal is usually modeled.
They are described not as particles, but as as "standing waves" that bounce
back and forth between the nearly perfectly reflecting walls of a crystal.

> Is it possible you're building an elecron laser?

Oops.  The problem is that electrons are fermions.  That is, electrons are
particles that just _don't_ like to be in the same place  at the same time.
Nor do they like to have the same momentum (energy) while they are bouncing
back and forth wave-style within the same metal crystal.  (Since in QM the
wavelength is inversely proportional to momentum, the latter statement is
equivalent to saying that electrons and other fermions "don't like to have
the same wavelength (energy) inside the crystal."

In contrast, the photons that are involved with lasing are bosons.  That
basically means that they love to do things together -- give them half a
chance, and they will all hop into the same region of space at the same
time, and will travel with the same momentum (wavelength).

This latter tendency of bosons to cluster together is the key to why lasers
work.  Basically, one photon start through a medium that's "loaded for bear"
and just itching to fire off many, many more photons of that same type.
But because they are bosons, the first photon is able to "entice" other
incipient photons to join it in perfect lockstep -- that is, with the same
direction, same phase, and same energy (momentum).  An interesting aspect
of boson statistics is that the more photons join in, the more tempting
it becomes for the next photon to join in, also.  I guess you could say
that bosons are real party animals, except that unlike most party animals
they insist on dressing and acting absolutely identically.

The final result is a sort of phenomenally well-ordered avalanche of bosons
that all share the same direction, energy (momentum), and phase.  That is,
they become a burst of coherent laser light.


Alas, for electons none of this group behavior can occur.  Electrons are
antisocial -- so much so that the level of energy required to force them
into _exactly_ the same location and momentum is nominally infinite.  The
electrons in the same metal crystal will do just about _anything_ to stay
out of step and out of each other's space, even if they have to climb all
over each other to do it.

And in fact, that is literally what they do.  A few poor electrons are
mercilously mashed into the lowest possible momentum and energy states
in the metal crystal (meaning that they move very, _very_ slowly, if at
all), while other electrons pile on top energy-wise to reach higher and
higher levels of momentum.

The net result of this fermion "anti-lasing" effect is altogether different
from what happens with bosons in the same situation.  Instead of flocking
together, the anti-social electrons spread out into a broad energy pile
that is more commonly known as a "band."

By that time the king-of-the-mountain electrons emerge on top of this
unfriendly electron energy heap, their velocities may be a large fraction
of the speed of light.  Hot stuff for a cold piece of metal! (The place
where the pileup ends is called the "Fermi surface," by the way.)

So why don't you get burned by these very hot electrons when you touch a
piece of metal?  Because they have no place to go to after they "dump"
their energy -- the lower levels of the energy pile are already filed up
with slower-moving electrons.  Just as a lake on a high plateau has stored
energy that can be used _only_ if you can find a way to let that water
flow down to some lower place, the extremely energetic Fermi surface
electrons simply cannot release any of their energy as long as all of
the energy spaces below them are filled up.

Thus the X-ray energy level electrons that are at this moment circling
your ring finger at nearly the speed of light turn out to be harmless
puffballs.  They are held back from doing finger-frying hard radiation
damage only by the presence of all those slow pokes sitting underneath
them.  (But if the rest of the band disappeared for just an instant...!)

If you want to see some of these very-fast, "king of the mountain" electrons
in action, just look at any piece of shiny metal.  Because the highest level
electrons are the _only_ ones with any room left to maneuver in, they are
the only ones in the heap (band) that that can absorb and re-emit photons --
that is, they are the ones that reflect light.

So while electrons cannot lase, we have all been looking at and using
examples of electron "anti-lasing" all of our lives.  It's an interesting
thought to keep in mind the next time you look at your own image being
reflected from the the metallic backing of a mirror.

....

So can this banding behavior be made into anything else interesting?  It's
hard to say, really.  But fermion banding is a lot of fun and an intriguing
effect, the sort of thing that makes solid state physics so fascinating.

				Cheers,
				Terry


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