I seek comments on the following. I believe JSD had something to say
about this not too long ago, but I'll bring it up again now that I'm
teaching it.
The de Broglie wavelength is defined by lambda = h/p. But K = p^2/2m,
so lambda = h/sqrt(2mK).
On the other hand, the thermal de Broglie wavelength is defined as
capital-lambda = h/sqrt(2*pi*mkT). This arises in the calculation of
the translational partition function of an ideal gas.
Comparing the two, we see they are the same if K=pi*kT. But it
doesn't seem to me that that is a good definition of "thermal average
value" of K; I would instead choose 1.5kT based on equipartition.
(You might argue I should instead average 1/K not K. I don't think
that will give me the factor of pi either, but you could try to
persuade me otherwise.)
Okay, 3/2 is close to pi. But my point is that I don't see why it
should be called the "thermal" de Broglie wavelength, when it is not
what I would consider the "thermal (average) value" of the "de
Broglie wavelength".
Definitions are what they are, but still why call it the "thermal"
wavelength when it isn't really? -Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/