Talk:Fermi energy

message: Fermi temperature is a stub right now, and doesn't contain any information that couldn't be easily shoehorned in here, especially since the concept is mentioned in this article.  I'm pretty new here, does anyone have thoughts? -- 7segment 01:49, 21 March 2006 (UTC)
replies: text: Good idea, I have just redirected it. Rex the first 12:35, 5 April 2006 (UTC)
replies: text:  Hmm, I think this was the wrong move.  The discussion of the Fermi temperature in this article is pretty well useless; you could probably derive the only result presented (that Tf=Ef/kB) simply by noticing that Boltzmann's constant was in units of joules per kelvin.  Personally, I think the Fermi temperature should have its own article.  I can contribute something to it...after I finish my physics assignment!  Ckerr 14:34, 26 August 2006 (UTC)

text:  Agreed. A separate article would be useful. Zebas (talk) 17:50, 14 December 2009 (UTC)
thread_title: Fermi temperature

message: The article presupposes that people are interested solely in 3-D fermi gases, which is a grave error. LeBofSportif 17:15, 5 June 2006 (UTC)
thread_title:  Dimensions 

message: What on earth is this article going on about? Can someone explain any of it so it makes sense to me? I have no idea about physics or anything like that.
: Sorry; there's not a whole lot that can be done.  The Fermi energy is not an easily graspable concept the way, say, momentum is, and I cannot off the top of my head see anything needlessly complicated in the way the article presents it.  Your best bet is to probably get an idea about physics, then try to read the article. Ckerr 14:37, 26 August 2006 (UTC)
replies: text: though there is nothing needlessly complicated about the introduction it assumes familiarity with many terms and concepts that are not 'required' to understand the concept of fermi energy. will try to remedy. --V. 18:23, 15 February 2007 (UTC)
thread_title: What?

message: But in the following calculation, no difference can be seen. So what does "divide this density into two" actually mean?    --Sandycx 08:09, 12 November 2006 (UTC)
thread_title:  About the Nucleus 

message: In the derivation for 3 dimensions the degeneracy of the fermions has implicitly been assumed to be 2. Whilst this is the case for electrons, it is not true in general, so I think it should be mentioned. Also, I think the line N = \frac{1}{8} \times 2 \times \frac{4}{3} \pi n_f^3 is poorly explained. My thoughts are: 
* the eighth is because we are in 3D and only want the eighth of the sphere in nx-ny-nz space where they are all positive,
* the 2 is the degeneracy which we have assumed is 2, which is not always the case,
* the four thirds pi nf is the volume of a spere of radius nf,
* and most importantly nf is never defined! It is  \sqrt{ \left( n_x^2 + n_y^2 + n_z^2\right) }.
As I'm new to wikipedia I thought I'd try to canvass opinion on whether adding this information would make the derivation too long before adding it. Uberdude85 01:30, 21 November 2006 (UTC)
thread_title:  Degeneracy isn't always 2, and more explanation of the derivation 

message: This article claims that the Fermi energy is identically equivalent to the chemical potential. I believe this is incorrect. The Fermi energy refers to the energy at the Fermi surface, which is equivalent to the chemical potential, in a non-interacting theory. In the presence of interactions, the Fermi surface can become fuzzed out, so that the Fermi energy is not well-defined.
The chemical potential, on the other hand, is a thermodynamic concept which is not concerned with any microscopic model for a system. It is defined even in classical statistical mechanics, in which there is no such thing as a "Fermi sea." -- CYD
:You may be right, at least about some of that. I went looking through my thermodynamics textbook (Sears & Salinger) for some ammunition, and was surprised to find a formula giving the chemical potential in terms of the Fermi energy:
::\mu = \epsilon _F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{\epsilon _F}\right) ^2 + \frac{\pi^4}{80} \left(\frac{kT}{\epsilon _F}\right)^4 + ... \right] 
:εF was introduced as an empirical constant and later defined in words as "the maximum energy of an electron at absolute zero". An F-D distribution function involving εF was given as a low-temperature approximation. However, the energy in the exact F-D distribution function is definitely the chemical potential from classical thermodynamics. Sears & Salinger gives a very detailed derivation of this. Although chemical potential was originally introduced in macroscopic thermodynamics, the relationship to microscopic theories (including Fermi seas!) is rigorously defined. You don't complain about temperature being invalid in microscopic theories, do you?
:That said, in solid state physics, I have often seen the F-D distribution given involving EF instead of μ -- hence my confusion here and on Fermi-Dirac statistics. I'll think about fixing the articles, but I haven't really got it straight in my head yet. -- Tim Starling
:after several days calculation, i still can't obtain the coefficient in the second term of the series mentioned above, and i can't find the derivation in Sear and Salinger also. Would any body suggest me for further reaing?tobywhc 13:11, 10 December 2006 (UTC)
replies: text: Ashcroft and Mermin has a fine derivation of the first two terms of the expansion on pp. 42-47. I also agree that the relevant quantity in the F-D distribution is the chemical potential rather than the Fermi energy. Reasoning naively, it makes sense that the finite T value of \mu is lower than the Fermi energy because the band structure has spherical symmetry. This means that there are more states slightly above the Fermi energy than slightly below, and consequently that the point of half-filling drops as you smear out the Fermi edge. Csmallw (talk) 22:11, 19 May 2009 (UTC)

text: actually the chemical potential at zero temperature is (almost by definition) equal to the Fermi energy. this is true even for a system with a more complicated potential, there the fermi surfave can become complicated but the fermi energy, the energy of the highest occupied state (@ T=0) is still unique. --V. 18:23, 15 February 2007 (UTC)
thread_title: Chemical potential

message: I think article should be expanded to include any half integer fermion case, instead of concentrating only on spin 1/2 particles  —Preceding unsigned comment added by 203.197.196.1 (talk) 23:27, 23 April 2008 (UTC)
thread_title: Incluse general spin states

message: I have started an article on quasi Fermi level, it needs work and is not ready for a "prime time", but when it is I think a link would be appropriate. --Thorseth (talk) 21:40, 20 May 2008 (UTC)
thread_title: Quasi Fermi levels

message: If I understand correctly, doing an analogous derivation at finite temperature for sufficiently low density would yield a Maxwell distribution.  If this is correct, it seems worth mentioning.  It connects it to something more familiar to many.  It can be explained where that approximation fails, and why it matters that the particles are fermions. 72.75.67.226 (talk) 03:55, 8 October 2009 (UTC)
thread_title:  Relationship to Maxwell distribution 

message: "...,all the energy levels up to n=N/2 are occupied and all the higher levels are empty."
What if the number of particles N is not an even number?
Andres.felipe.ordonez (talk) 00:58, 17 January 2012 (UTC)
thread_title:  Even number of particles in the square well example 

message: I'm proposing a merge between Fermi energy page and Fermi gas into one page (Fermi gas) as the former is a subproperty of the latter concept. This proposal also takes in fact the Fermi energy article has better equations and is better explained than the Fermi gas article so mostly the new merged article won't lose any generality. MaoGo (talk) 17:44, 4 January 2018 (UTC)
replies: text: I think that the content of Fermi energy should be merged into Fermi gas. However I also think that a short stub should be kept at Fermi energy with just a formula and a brief explanation. Ruslik_Zero 19:15, 4 January 2018 (UTC)
replies: text:  That is a good idea. While it is true that the Fermi energy is a concept based on a non-interacting Fermi gas, Fermi level and Fermi energy are often used interchangably and it's good to keep the discussion of the differences between the two as part of a separate small article. --Mark viking (talk) 19:44, 4 January 2018 (UTC)
replies: text:  Maybe we can leave a stub, but I'm not sure if it is a good idea. In think Fermi level does pretty well alone, while Fermi energy (and other related terms like Fermi temperature) can be redirected to a major section in Fermi gas. MaoGo (talk) 19:56, 4 January 2018 (UTC)

text: At risk of getting sidetracked, "Fermi energy is the chemical potential of an electrically charged moiety" is indeed one definition of Fermi energy, but it's not the only definition, and in particular it's not the definition currently used for the Fermi energy article. See this page of my website for example. Your definition, "the chemical potential of an electrically charged moiety", is instead covered in the Fermi level article. --Steve (talk) 14:45, 5 January 2018 (UTC)
replies: text: All definitions reduce to the thermodynamic definition. Xxanthippe (talk) 23:27, 5 January 2018 (UTC)

text: As others suggested we can leave Fermi energy article alive to discuss this kind of definition problems, but this merge is not even about that, it is about getting Fermi gas calculations into the right article.  — Preceding unsigned comment added by MaoGo (talk • contribs) 20:44, 6 January 2018 (UTC)
thread_title:  Merge with Fermi gas 

message: Re: recent changes by  with "we don't typeset grammatical commas in the equations" − who are "we" and why they don't? AFAIK, as a rule, scientific papers do use normal English grammar. E.g., https://www.e-education.psu.edu/styleforstudents/c4_p3.html Evgeny (talk) 18:13, 3 December 2021 (UTC)
replies: text: Duly noted. I see this is an oft-debated topic (the link you posted, along with some other sources), and the usage depends on the exact structure of the sentence and typesetting. It looks confusing at times when the punctuation is in the formula (when the formula is not in line with prose, in which case there doesn't seem to be any confusion), so some authors circumvent it by changing the sentence structure. If I (unknowingly) went against a convention, which seems like common practice but not universal as some other rules, please revert my edits without further ado. ComplexRational (talk) 19:57, 3 December 2021 (UTC)
replies: text: OK, thanks; frankly, I feel rather strongly about this, so will revert your edits. Evgeny (talk) 22:42, 3 December 2021 (UTC)
thread_title:  Grammar rules and equations