GR8677 #55


Problem



Statistical Mechanics}Fermi Temperature
When one deals with metals, one thinks of Fermi brandingi.e., stuff like Fermi energy, Fermi velocity, Fermi temperature, etc. So, . Fermi stuff is based on the FermiDirac distribution, which assumes that the particles are fermions. Fermions obey the Pauliexclusion principle. (c.f. BoseEinstein distribution, where the particles are bosons, who are less discriminating and inclusive than fermions. Both BoseEinstein and FermiDirac assume indistinguishable particles, but the Boltzmann distribution, which assumes the particles are distinguishable)
All the other choices are too general, since bosons can also satisfy them. (Moreover, the Born approximation is pretty much the fundamental assumption of all of QMevery single calculation you do involving the interpretation of mod square of wave functions as probability depend on the Born approx!)


Alternate Solutions 
SillyMan 20130619 21:54:37  The best solution is the following: At zero temperature, fermions must occupy the lowest energy states up to the Fermi energy. These states have finite energy.
(Finite/Zero) >> 1.
In other words, (/kT) >> 1.  

Comments 
fredluis 20190917 02:10:41  Sounds interesting enough; maybe I\'ll watch out for this kind of solution. carpet cleaners   ernest21 20190823 02:03:12  The divergence of the polarization is related to the total charge density, not the surface charge density. cyclone insider   SillyMan 20130619 21:54:37  The best solution is the following: At zero temperature, fermions must occupy the lowest energy states up to the Fermi energy. These states have finite energy.
(Finite/Zero) >> 1.
In other words, (/kT) >> 1.
SillyMan 20130619 21:55:38 
(/kT) >> 1*

  pt6 20120820 10:03:28  Why degeneracy of states is not appropriate choice?   jw111 20080914 12:02:24  One atom has many discrete energy level. [1 2 3 4 5 ...]
=>Without energy apply, electron occupy the energy level from the lowest[ [x x x 4 5 ...]
When two identical atom come to joint together, we can't have somthing likes
[x x x 4 5 ...]
[x x x 4 5 ...]
because of the Pauliexclusion principle; electrons can't have the same quantum state in our new molecule. The solution taked by nature is
[x x x 4 5 ...]
[x x x 4.1 5.1 ...]
that is, to our molecule, the energy level becomes
[1 1.1 2 2.1 3 3.1 4 4.1 5 5.1 ......]
When you have 1 mole atoms to form a bulk material, the energy level seems continuethe energy band.
It is Pauliexclusion principle forcing that electrons can't behave like classical particles when assigning mechanical states.   Blake7 20070722 20:50:32  I actually left this one blank on a practice run because I couldn't quickly resolve that the Born Approximation (for Xsections) isn't applicable here to an electron gas of 'Paulions'
Truth is, I couldn't remember offhand what the Born approximation was, either; now it comes back to me. Moral of the story; under a "No Guesses" strategy, I couldn't gain the point.   wzm 20061103 11:24:08  The electrons form a Fermi Gas. The Pauli exclusion principle keeps electrons from all occupying the ground state in momentum space, and pushes them into higher energy states.
SonOfHam 20101112 00:43:52 
Yes, this is the most direct answer. In these problems, quick qualitative reasoning is best.

flyboy621 20101114 21:33:11 
yes

tatitechno 20110921 07:32:53 
good (the best answer)

Astronaut 20160219 11:06:51 
Yup

  einstein 20060329 21:22:13  Just a clarification of the comment you make at the end>
(Moreover, the Born approximation is pretty much the fundamental assumption of all of QMevery single calculation you do involving the interpretation of mod square of wave functions as probability depend on the Born approx!)
I think you are confusing the "Born Probability interpretation" (ie that the mod square of the wave function= probability density) with the "Born Approximation" (which essentially means to take only the first term in a perturbative series solution to a scattering problem).
nitin 20061116 09:06:51 
Yes, Yosun's rant about the Born Approximation is definitely wrong. The Born Approximation amounts to taking the first term in the Born expansion. Careful Yosun!

SurpriseAttachyon 20150915 21:28:29 
These forums have made me a lot more confident about my physics abilities... Watching obvious mistakes among the pros is comforting

 

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