Re: Whence Degeneracy Pressure?

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

kowalskil wrote:
> In other words, we should avoid topics like this unless students
> (and ourselves) are familiar with quantum mechanics, etc. Right?

Are you hesitant to admit that there are some things
in the universe that you don't understand from first
principles?  I'm not.

Actually, one doesn't even need to admit anything.  It
suffices to say that such-and-such is beyond the scope
of the course.  In a course on Newtonian mechanics, it
is appropriate to say
 -- We are not going to cover laser physics.
 -- We are not going to cover semiconductor band structure.
 -- We are not going to cover neurosurgery.
 -- We are not going to cover oil-painting or bronco-busting.
 -- And we are definitely not going to cover very much
    detail about the degenerate Fermi gas.


Newtonian physics is only an approximation to the real
(quantum) physics.  As with any approximation, it is very
important to be able to recognize the limits of validity
(although this important topic is often neglected).  I
can recognize a wild horse when I see one, but I'm not
required to ride it.  By the same token, you need to
know enough about quantum mechanics to be able to
recognize a quantum problem, even if you aren't going
to actually solve it.  Classical mechanics will, alas,
not tell you the limits of its own validity.

In the present case, you don't even need to know
anything!  If the creature comes to you with a big
sign around its neck saying "wild horse" you should
not be too surprised if it turns out to be a wild
horse.  If a problem comes to you labeled "degeneracy"
you should not be too surprised if it turns out to
be a nonclassical problem.  It's nonclassical by
definition, by construction.

One might ask a more general question, about how to
ascertain the limits of validity of classical mechanics
in general.  That's a totally nontrivial question, and
I'm not going to discuss it right now.