Talk:Fermi-Dirac statistics

Awesome plots, Unc.hbar. My plot was thrown together quickly, with the intent of spurring someone else to make a better one. I see the plan worked in record time. Ed Sanville 14:27, 14 May 2005 (UTC)

Is the word "statistics" plural? I think so, but Florian Marquardt introduced some grammar suggesting it's singular. He also left in some of my plural forms, leaving the article sounding rather confused. I've changed it to be consistently plural. If anyone knows better please say so.

Also, F-D statistics are used for electrons in solids, not just electrons generally. In free space, you don't usually need QM, and inside atoms or molecules, you need non-statistical QM. -- Tim Starling

Electrons can be be found in other forms than 'in solids' or 'in free space', there are in every (non-solid/non gas) molecule also.

Oh really? Perhaps that's why I wrote above "inside atoms or molecules, you need non-statistical QM". I guess there could be applications for F-D statistics for electrons in molecular or atomic gases – perhaps at high temperatures – but informing me smugly that there are electrons in liquids and gases is probably not the best way to start such a discussion.

Sorry, I had not intention of being sarcastic or offending, I just wanted to state that solid-state physics]] is not the only field where F-D apply; i.e. F-D seems to be used in dense-matter physics, white-dwarf & neutron star are also (but not so good) example. - looxix 22:36 Mar 3, 2003 (UTC)

I didn't mean to suggest that F-D statistics can never be used for liquids or gases. I thought the statement "F-D statistics applies in particular to the electrons and therefore are often used in the study of solids" was misleading. It implies that anything containing electrons is suitable for study with F-D statistics. This is certainly untrue. -- Tim

F-D statistics is not only used for electrons in solids, in fact, a metal conductor is better interpreted as a 'gas' of electrons embedded in a solid mesh/lattice (see Fermi gas).

The "gas" analogy may be a useful one, but it does miss some of the more curious properties of solids. Although a small fraction of the electrons in a metal are free to move and respond to external forces (like the particles of a classical gas), not all of them are. Why not? -- Tim

I didn't say that all electrons are part of the "gas". - looxix 22:36 Mar 3, 2003 (UTC)

also F-D (as B-E) statistics apply to indistinguishable particle, if the electrons are bound in a solid, then they are distinguishable.

of course I may be totaly wrong. - looxix 22:14 Mar 2, 2003 (UTC)

About that last point, yes unfortunately you are "totaly wrong". Electrons are always indistinguishable. See identical particles for a sketchy explanation. -- Tim Starling 04:29 Mar 3, 2003 (UTC)

Indeed, I confounded with nuclei in a crystal. - looxix 22:36 Mar 3, 2003 (UTC)

Derivation

The new "derivation" is NOT a derivation of Fermi-Dirac statistics. The "another derivation" is much closer to a derivation, since it starts from statistical assumptions and statistical relationships. Any derivation that does not introduce the statistics of how indistinguishable particles are distributed among various energy levels while assuming each distribution is equally likely, is not a derivation. The present "derivation" introduces the partition function as a given! The partition function follows naturally from a statistical analysis of Fermions and is not a given!. The present "derivation" introduces the probability of an electron having a particular energy as a given, but this is just what a derivation is supposed to derive! This is not a derivation. It needs to go somewhere else, under a different title. By removing it I don't mean to seem like I am throwing it out, I just don't know quite where it fits. PAR 01:31, 15 May 2005 (UTC)

Yes, I am taking partition function for granted because in science we prove something once and then use it again and again. One can look up derivation of the partition function if (s)he so desires. Also, someone looking up FD statistics in Wikipedia rather than SM text would more easily follow my logic than yours. Feel free to change the title, please don't erase my work. Unc.hbar 02:08, 15 May 2005 (UTC)

Do you like my plots? Unc.hbar 02:21, 15 May 2005 (UTC)

I am reading and rereading what you wrote, and I cannot follow it. You say energy is 0 or epsilon, and use this, then later bring in the chemical potential from I don't know where, to fix the fact that energy is not zero. You say gi is unity, but then later say you don't need to put it in because its "put in later", implying it is not unity. When you say n-bar is a probability, you have to have a level subscript, or else its an integral, and then its not a probability. It just needs tons of work before it makes any sense. This is not to say that the second derivation is clear as a bell. It needs work too. PAR 03:14, 15 May 2005 (UTC)

It is a well-known fact that energy can be offset without significant implications to the problem, I don't see why I can't slip <math>\mu<math> in at the last moment :). I don't like carrying the degeneracy around since it only multiplies the answer at the end. I am not a fan of subscripts, which is odd because I study GR.

Statistical Mechanics is a bunch of hand-waving. There are 2 kinds of hand-waving: (1) rigorous; (2) non-rigorous. Title my stuff as "non-rigorous hand-waving" if you will. We could just cut and paste the book. I think the idea if this website is to provide something books can't/don't.

I agree, the "derivation" is not crystal clear, I'll keep working on it.

I think my stuff is more undergraduate, yours is graduate-level. Maybe we should title them so? How's FD for Dummies and FD for Hard-Core Physicists?

Also, I think the plots are excellent. I fixed the captions for mu and epsilon. I tried to do something similar with the Bose gas article. What did you use to make the plots?

Thanks. I used SM (Supermongo). hbar 03:47, 15 May 2005 (UTC)