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This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 January 2022 and 18 March 2022. Further details are available
on the course page. Student editor(s):
Tenzzor,
Hcontr (
article contribs).
This article should make it obvious that it (mostly) applies to covalently bonded crystalline solids. (Though non-crystalline covalent solids also have band structure.) It mostly does not apply to molecular solids, where individual molecules are held together by weaker bonds, with little electron overlap between them. Gah4 ( talk) 21:54, 10 October 2020 (UTC)
Does it say in the article, or explain well enough, that full bands don't contribute to conduction? I wanted to link to it, but I don't see it. Gah4 ( talk) 16:29, 1 February 2021 (UTC)
There is some sort of confusion about the meaning of the Pauli principle here. I added a request for a citation near the invocation of the Pauli principle. The statement about the Pauli principle is now gone from the main text, but still exists in the figure caption. I already edited the Pauli principle out once in December, but this change was reverted, with a message "This is an elementary explanation for general readers. It should include that the underlying reason for the splitting of the energy levels is the Pauli exclusion principle". But the point is not about elementary vs. technical, it is about factually correct statements and clear concepts. If you invoke the principle, I would ask you to at least provide a textbook reference in which it is used in the calculation of the band structure.
How I view the role of the Pauli principle technically: the crystal is a many-body system, but with the simplifying assumption no interactions, we can describe the many-body states in terms of single-particle states. The band structure calculation then reduces to an application of Bloch's theorem for a single-particle Schrödinger equation. Thus, there is no Pauli principle at this point, only hybridization.
Now, to describe the filling of the bands, we have to revert back to many-body description, and here we encounter the Pauli principle. It tells us that our terminology makes sense; the states indeed become "filled" and we cannot put a second electron to the same state. I think it will benefit even the elementary reader if these two things, the formation of the band structure and how the electrons occupy it, are presented as separate concepts and the principle is invoked only for the latter one. - Jähmefyysikko ( talk) 06:22, 5 February 2022 (UTC)
Exactly, thanks for the clarification. Jähmefyysikko ( talk) 15:23, 5 February 2022 (UTC)
The article says: When two identical atoms join to form a molecule, their atomic orbitals overlap. This at least needs to allow for compound semiconductors. It works for any crystal made of identical or not atoms. And for many non-crystalline materials, too. Gah4 ( talk) 19:32, 18 July 2023 (UTC)
I removed the statement about Pauli principle. It was supported by two references (Holgate and Van Zeghbroeck). The first one is a semi-popularized textbook and the second one is self-published. Stardard textbooks (Kittel, Ashcroft & Mermin, Oxford Solid State basics) do not invoke Pauli Principle when describing the band formation. Jähmefyysikko ( talk) 09:00, 23 September 2023 (UTC)
I added the phrase mentioning the Pauli exclusion principle to the caption of the graph, which was removed by
Jähmefyysikko.
My version:
Jähmefyysikkos version:
Which is better? -- Chetvorno TALK 05:19, 8 November 2023 (UTC)
The Pauli Exclusion Principle prohibits them from having the same energy. The Pauli principle forbids two electrons from occupying the same quantum state. But two states can be degenerate and have the same energy, and still be simultaneously occupied. Jähmefyysikko ( talk) 08:48, 8 November 2023 (UTC)
References
This is the
talk page for discussing improvements to the
Electronic band structure article. This is not a forum for general discussion of the article's subject. |
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|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Archives:
Index,
1Auto-archiving period: 90 days
![]() |
![]() | Text and/or other creative content from this version of Energy band was copied or moved into Electronic band structure with this edit on 01:24, 7 September 2006. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
![]() | Text and/or other creative content from this version of Band theory was copied or moved into Electronic band structure with this edit on 00:42, 10 September 2006. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
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A graph should have been displayed here but
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This page has archives. Sections older than 90 days may be automatically archived by ClueBot III when more than 5 sections are present. |
This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 January 2022 and 18 March 2022. Further details are available
on the course page. Student editor(s):
Tenzzor,
Hcontr (
article contribs).
This article should make it obvious that it (mostly) applies to covalently bonded crystalline solids. (Though non-crystalline covalent solids also have band structure.) It mostly does not apply to molecular solids, where individual molecules are held together by weaker bonds, with little electron overlap between them. Gah4 ( talk) 21:54, 10 October 2020 (UTC)
Does it say in the article, or explain well enough, that full bands don't contribute to conduction? I wanted to link to it, but I don't see it. Gah4 ( talk) 16:29, 1 February 2021 (UTC)
There is some sort of confusion about the meaning of the Pauli principle here. I added a request for a citation near the invocation of the Pauli principle. The statement about the Pauli principle is now gone from the main text, but still exists in the figure caption. I already edited the Pauli principle out once in December, but this change was reverted, with a message "This is an elementary explanation for general readers. It should include that the underlying reason for the splitting of the energy levels is the Pauli exclusion principle". But the point is not about elementary vs. technical, it is about factually correct statements and clear concepts. If you invoke the principle, I would ask you to at least provide a textbook reference in which it is used in the calculation of the band structure.
How I view the role of the Pauli principle technically: the crystal is a many-body system, but with the simplifying assumption no interactions, we can describe the many-body states in terms of single-particle states. The band structure calculation then reduces to an application of Bloch's theorem for a single-particle Schrödinger equation. Thus, there is no Pauli principle at this point, only hybridization.
Now, to describe the filling of the bands, we have to revert back to many-body description, and here we encounter the Pauli principle. It tells us that our terminology makes sense; the states indeed become "filled" and we cannot put a second electron to the same state. I think it will benefit even the elementary reader if these two things, the formation of the band structure and how the electrons occupy it, are presented as separate concepts and the principle is invoked only for the latter one. - Jähmefyysikko ( talk) 06:22, 5 February 2022 (UTC)
Exactly, thanks for the clarification. Jähmefyysikko ( talk) 15:23, 5 February 2022 (UTC)
The article says: When two identical atoms join to form a molecule, their atomic orbitals overlap. This at least needs to allow for compound semiconductors. It works for any crystal made of identical or not atoms. And for many non-crystalline materials, too. Gah4 ( talk) 19:32, 18 July 2023 (UTC)
I removed the statement about Pauli principle. It was supported by two references (Holgate and Van Zeghbroeck). The first one is a semi-popularized textbook and the second one is self-published. Stardard textbooks (Kittel, Ashcroft & Mermin, Oxford Solid State basics) do not invoke Pauli Principle when describing the band formation. Jähmefyysikko ( talk) 09:00, 23 September 2023 (UTC)
I added the phrase mentioning the Pauli exclusion principle to the caption of the graph, which was removed by
Jähmefyysikko.
My version:
Jähmefyysikkos version:
Which is better? -- Chetvorno TALK 05:19, 8 November 2023 (UTC)
The Pauli Exclusion Principle prohibits them from having the same energy. The Pauli principle forbids two electrons from occupying the same quantum state. But two states can be degenerate and have the same energy, and still be simultaneously occupied. Jähmefyysikko ( talk) 08:48, 8 November 2023 (UTC)
References