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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)
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)
I am a little confused about the vector term in the 3d model. Based on the since the n value has to be a positive integer, why is it necessary to have an absolute value of the vector? If all components of the vector are positive, how could the vector be negative? Methinks I am missing something. Good article btw. -Hellkyte
You don't seem to understand the concept of a vector very well. A vector is not a number, so there cannot be a number of states less than or equal to a vector; the notion of less than or equal to a vector does not even make sense because there is no canonical ordering on vectors in 3-dimensional Euclidean space. "Absolute value" is also sort of a misnomer; the |s represent the operation of taking the magnitude of the vector, which is sort of like the absolute value of a number (the two coincide on the real numbers), but not quite the same. "[why?]" removed. — Preceding unsigned comment added by 75.161.171.91 ( talk) 21:35, 4 April 2015 (UTC)
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.
In my opinion the starting part of this article (the introduction) is clear and very easy to understand. This is in contrast with many (most?) other physics related articles I have read so far. Most of them generally suppose that the reader actually already knows everything about the matters discussed in the particular article. This article doesnt suppose any more than very basic prior knowledge about it's subject. Congratulations to the author(s). It would be very nice if more of the physics related articles were like this one.
--- Hey, I totally agree. Compared to the German graduate book I've read before this really helped me a lot! Especially the derivation of the three-dimensional potential is very well introduced and structured!
Now since the fermi energy only applies to fermions of the same type, one must divide this density in two. This is because the presence of neutrons does not affect the fermi energy of the protons in the nucleus.
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)
Since it looks like the above was dealt with (area in the derived formula = .5 the norm), could someone please explain the justification for dividing by two, seeing as #protons != #neutrons in atoms? I feel like the derivation assumes that, which isn't true for many atoms. Doing a correction of the area for a specific nucleon based on the atomic makeup for an atom isn't terribly difficult, although it would add a couple extra lines. Just seems wrong to make this poor of an assumption to avoid a little extra derivation. Maybe I am missing something though, I am but a lowly chemist. -Hellkyte
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 is poorly explained. My thoughts are:
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)
I'd like to take issue with the statement that Fermi energy is the energy of the highest filled state at T=0. If the highest filled state just happens to fill a band, then the fermi energy (the electrochemical potential) is mid-gap. Should this be changed? —Preceding unsigned comment added by 163.1.18.226 ( talk) 17:56, 7 February 2010 (UTC)
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
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)
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)
I think it's a serious error to state that chemical energy (but not electrochemical energy) is equal to Fermi energy at absolute temperature. Does the author mean ELECTROCHEMICAL energy?
Because that makes sense.
!! I see the error now. Throughout the article CHEMICAL potential is used for ELECTROCHEMICAL potential. But they are very different concepts.
Chemical potential has to do with doping, whereas electrochemical potential gives rise to the electromotive force.
I suggest we fix this error.
I see that my concern has been brought up before by CYD. He's right and he has put the problem better than me. If nobody is willing to correct this serious error, I am going to do it
128.46.213.219 ( talk) 20:45, 22 August 2008 (UTC)
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)
"...,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)
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)
For us lazy-bones, it would be nice to have typical values for the fermi momentum too. So, for example, for metals, I think, maybe, that the fermi momentum, is less than a few inverse angstroms, i.e. less than the interatomic spacing, right? But it would be nice to know without having to whip out my calculator, and googling around. (and what about the fermi temperature? What might that be?) and out of shear curiosty, same for white dwarves, nuclei. And neutron stars? 162.204.250.21 ( talk) 02:05, 12 August 2019 (UTC)
Re: recent changes by ComplexRational ( talk · contribs) 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)
The second sentence of the first paragraph currently states: 'In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy'.
Is that a simplification? Wouldn't it in fact have a non-zero kinetic energy due to the uncertainty principle? MathewMunro ( talk) 13:09, 6 January 2024 (UTC)
Recent edits on proton remind me that quarks and gluons should also have a Fermi energy inside the nucleon. Maybe that can be given here, including an approximate Fermi energy. Gah4 ( talk) 20:19, 27 March 2024 (UTC)
This
level-5 vital article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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)
I am a little confused about the vector term in the 3d model. Based on the since the n value has to be a positive integer, why is it necessary to have an absolute value of the vector? If all components of the vector are positive, how could the vector be negative? Methinks I am missing something. Good article btw. -Hellkyte
You don't seem to understand the concept of a vector very well. A vector is not a number, so there cannot be a number of states less than or equal to a vector; the notion of less than or equal to a vector does not even make sense because there is no canonical ordering on vectors in 3-dimensional Euclidean space. "Absolute value" is also sort of a misnomer; the |s represent the operation of taking the magnitude of the vector, which is sort of like the absolute value of a number (the two coincide on the real numbers), but not quite the same. "[why?]" removed. — Preceding unsigned comment added by 75.161.171.91 ( talk) 21:35, 4 April 2015 (UTC)
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.
In my opinion the starting part of this article (the introduction) is clear and very easy to understand. This is in contrast with many (most?) other physics related articles I have read so far. Most of them generally suppose that the reader actually already knows everything about the matters discussed in the particular article. This article doesnt suppose any more than very basic prior knowledge about it's subject. Congratulations to the author(s). It would be very nice if more of the physics related articles were like this one.
--- Hey, I totally agree. Compared to the German graduate book I've read before this really helped me a lot! Especially the derivation of the three-dimensional potential is very well introduced and structured!
Now since the fermi energy only applies to fermions of the same type, one must divide this density in two. This is because the presence of neutrons does not affect the fermi energy of the protons in the nucleus.
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)
Since it looks like the above was dealt with (area in the derived formula = .5 the norm), could someone please explain the justification for dividing by two, seeing as #protons != #neutrons in atoms? I feel like the derivation assumes that, which isn't true for many atoms. Doing a correction of the area for a specific nucleon based on the atomic makeup for an atom isn't terribly difficult, although it would add a couple extra lines. Just seems wrong to make this poor of an assumption to avoid a little extra derivation. Maybe I am missing something though, I am but a lowly chemist. -Hellkyte
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 is poorly explained. My thoughts are:
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)
I'd like to take issue with the statement that Fermi energy is the energy of the highest filled state at T=0. If the highest filled state just happens to fill a band, then the fermi energy (the electrochemical potential) is mid-gap. Should this be changed? —Preceding unsigned comment added by 163.1.18.226 ( talk) 17:56, 7 February 2010 (UTC)
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
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)
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)
I think it's a serious error to state that chemical energy (but not electrochemical energy) is equal to Fermi energy at absolute temperature. Does the author mean ELECTROCHEMICAL energy?
Because that makes sense.
!! I see the error now. Throughout the article CHEMICAL potential is used for ELECTROCHEMICAL potential. But they are very different concepts.
Chemical potential has to do with doping, whereas electrochemical potential gives rise to the electromotive force.
I suggest we fix this error.
I see that my concern has been brought up before by CYD. He's right and he has put the problem better than me. If nobody is willing to correct this serious error, I am going to do it
128.46.213.219 ( talk) 20:45, 22 August 2008 (UTC)
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)
"...,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)
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)
For us lazy-bones, it would be nice to have typical values for the fermi momentum too. So, for example, for metals, I think, maybe, that the fermi momentum, is less than a few inverse angstroms, i.e. less than the interatomic spacing, right? But it would be nice to know without having to whip out my calculator, and googling around. (and what about the fermi temperature? What might that be?) and out of shear curiosty, same for white dwarves, nuclei. And neutron stars? 162.204.250.21 ( talk) 02:05, 12 August 2019 (UTC)
Re: recent changes by ComplexRational ( talk · contribs) 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)
The second sentence of the first paragraph currently states: 'In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy'.
Is that a simplification? Wouldn't it in fact have a non-zero kinetic energy due to the uncertainty principle? MathewMunro ( talk) 13:09, 6 January 2024 (UTC)
Recent edits on proton remind me that quarks and gluons should also have a Fermi energy inside the nucleon. Maybe that can be given here, including an approximate Fermi energy. Gah4 ( talk) 20:19, 27 March 2024 (UTC)