Talk:Slater determinant

It might be worth adding a comment about how Slater determinants and Hartree products have the same eigenfunctions with a one-electron hamiltonian (because SDs are linear combinations of HPs) - might make the use of SDs seem more reasonable. Also perhaps a note on how antisymmetry can be enforced in a different way using second quantization. Cdr Harris Fan Club 14:57, 21 Jun 2004 (UTC)

I changed the normalization factor in the example to 1/SQRT(2!) instead of 1/SQRT(3!), because it is about two fermions

what is "phi"?

It states in the article's very first sentence that it satisfies one the requirements of anti symmetry- that "phi" = 0, but does not define "phi" at all. What is "phi"? Need to clean up the language here a bit. — Preceding unsigned comment added by 24.30.94.84 (talk) 01:42, 11 August 2011 (UTC)

Wedge Product

Could someone please elaborate on how a Slater determinant is the wedge product (as defined in a more general mathematical setting). — Preceding unsigned comment added by 2.222.44.210 (talk) 18:31, 1 November 2011 (UTC)

I would have to guess, but since a wedge product can be written as a determinant, someone (maybe even the author of a textbook) thought it would be beneficial to note that the inverse is also true. Lpd-Lbr (talk) 09:11, 16 September 2019 (UTC)

Nomination for worst sentence ever:

Therefore the Hartree product does not satisfy the Pauli principle; that is to say: on the one hand, the interchange of fermions must give rise to negation of the wave function because fermions must have antisymmetric wavefunctions, yet on the other hand, they should still be indistinguishable, meaning the exchange of particles does not change the results of measurements performed on the system and thus two particles cannot be distinguished from each other.

Can somebody who knows what it's actually trying to say fix it? — Preceding unsigned comment added by 184.97.156.211 (talk • contribs)

Does my edit help? --Bduke (Discussion) 22:59, 11 June 2013 (UTC)

Much better. Thank you. — Preceding unsigned comment added by 184.97.156.211 (talk) 14:57, 12 June 2013 (UTC)

Alleged conflict of interest

To Second Quantization: Please explain why you deleted an apparently reasonable paragraph with the edit summary COI self promotion. The paragraph in question was added by editor Wdlang on 4 July 2014, while the scientific paper used as source was authored by J M Zhang and Marcus Kollar, so it is not obvious that there is a COI. If there is a relationship between Lang, Zhang and Kollar which creates a COI, perhaps you could explain it. Some of us don't know any of these 3 persons. Dirac66 (talk) 00:53, 15 March 2015 (UTC)

I agree. I have reverted the edit until the COI is clarified. However, I think that paragraph could be simplified and shortened for clarity. --Bduke (Discussion) 01:41, 15 March 2015 (UTC)http://www.theage.com.au/victoria/victoria-to-ban-ewaste-in-landfill-20150314-13xxab.html

Did you not read his talkpage? The COI is acknowledged explicitly: "I do believe my results are of pedagogical value. ... I believe I understand the topics on which I have publications very well. But how should I prove that? ... I invite them to have a look of my paper. Of course, this is too much work for them, possibly. Anyway, I do believe my paper can help ... Of course they are related to my publications. It might sound cocky, but I really believe readers will find them helpful.". He's been adding his papers in multiple locations. That is clearly a conflict of interest. See wikiproject physics, Second Quantization (talk) 14:07, 15 March 2015 (UTC)

Thanks for your reply. I did in fact notice the above passage on User talk:Wdlang, but in this article on Slater determinant, he has not cited his own paper but rather the paper by Zhang and Kollar. His user contributions cover about 10 articles, so perhaps he meant that he had cited his own papers in other Wiki articles. But for this particular article I don't see that there is evidence of a COI. Dirac66 (talk) 15:04, 15 March 2015 (UTC)

" he has not cited his own paper ". ?? He is Zhang as far as I can see and has said as much Second Quantization (talk) 22:16, 16 March 2015 (UTC)

Ah, I had not realized that Wdlang is Zhang, since it is not clear from this article. My first reaction was to ask for your evidence, but I have now found evidence at Fermi's golden rule, where you recently deleted text added by Wdlang and referring to another article by Zhang (and Haque), and where the talk page has comments by Wdlang about "my paper" and "my derivation". So OK, I will now accept that Wdlang is Zhang.

However we still have to consider separately for each article whether the self-cite is acceptable under the guideline at WP:SELFCITE, which says:

Using material you have written or published is allowed within reason, but only if it is relevant, conforms to the content policies, including WP:SELFPUB, and is not excessive. Citations should be in the third person and should not place undue emphasis on your work. When in doubt, defer to the community's opinion.

In this case my opinion is that we have a 3-line mention of the relationship of Slater determinants to more general fermionic wave function, which does seem relevant to the article and not excessive. The phrase "it is an interesting problem" was perhaps puffery, but I have removed it. Do others think that this paragraph can now be retained, with or without minor changes? Bduke? Dirac66 (talk) 23:57, 16 March 2015 (UTC)

I agree that the 3-line mention can be retained. --Bduke (Discussion) 01:14, 17 March 2015 (UTC)

I was the one that originally brought this to the wiki editors attention. I disagree with the inclusion because there is nothing that distinguishes it from the immense amount of literature published on "Slater determinants." The fact that the editor, who is the author of the paper, thought that his work has such merit over all other literature to be included in the original papers strikes me as blatant self promotion. — Preceding unsigned comment added by 129.105.14.165 (talk) 23:02, 21 January 2016 (UTC)

Removed non sequitur

I removed the following and is open for discussion For didactic purposes, the Slater determinant can be evaluated by the Laplace expansion. Mathematically, a Slater determinant is an antisymmetric tensor, also known as a wedge product.

• All determinants can be laplace expanded. The reference to the laplace expansion of a determinant here can only be justified with a nice example, e.g. a block diagonal matrix (e.g 4 electrons coupled in pairs) where the two pieces of the slater matrix decompose in the two blocks of the determinant and where the laplace expansion can be visualized as block determinant.
• The statement about determinant = antysimmetric tensor looks ill formed: a determinant is antysimmetric,is precisely an invariant, but is not a tensor (there can be maybe an argument in 2D-3D), and the originating matrix is a linear form or a connection at best not a tensor either.
• The statement that the determinant is the wedge product is wrong, the determinant is only the last component of the wedge product, i.e. the directed volume. Namely is the coefficient in front of the pseudo scalar which is the last term in the wedge product.

The determinant is just one of the many invariants of a matrix or more generally of a linear form. The wedge product is a bi-linear map from the vector space V of dimension N (e.g. $R^{n}$) to the cotangent bundle which has dimension $2^{n}$ (e.g. see Differential Form), this space has also a grading, and for each subspace you can see the component/projection of the wedge product in that subspace, as a local directed volume in the subspace as you do for grassman algebras. This is also what is a multivector field . Therefore all this, although may be interesting, is not relevant here. As stated above it may be relevant to add a section on generic fermionic wave functions, or the relationship with grassmanniann and QFT.

References

Detailed example

Can somebody please add more intuition to the Detailed example [7], many electron problem. It seems that if all ri go to r (constant) or all Ri go to R, the energy explodes which doesn't seem to make physical sense. Isn't it so that there are repulsive forces between the particles? Is there a sign mistake or something? — Preceding unsigned comment added by 188.238.197.125 (talk) 21:24, 1 March 2021 (UTC)