# Talk:Clebsch-Gordan coefficients

From Wikipedia, I changed the lead, added equation for explicit expression (plus discussion) and one special case.--Paul Wormer 03:45, 22 August 2007 (CDT)

## Confusement

In the original WP text the *i* in *j*_{ i} could stand for *x*, *y*, or *z*, or for "particle number" 1 or 2. In some situations this was confusing, so I introduced *x*, *y* and *z*.--Paul Wormer 07:32, 7 October 2007 (CDT)

## Notation of eigenstates

Is there a difference between the states and ? I guess not, because the latter notation appears in the orthogonality relation

without any comment. I find it rather confusing that both notations appear in the definition

for the CG coeffs. -- Jitse Niesen 06:37, 30 July 2008 (CDT)

Incidentally, the book we used when learning quantum mechanics (Quantum Physics by Stephen Gasiorowicz) calls them Wigner coefficients; is it just a strange book or is that name really used or are Wigner coefficients something subtly different? -- Jitse Niesen 06:47, 30 July 2008 (CDT)

And another question: the edit history shows that the from-wp flag suddenly disappears. Was this done on purpose? -- Jitse Niesen 07:11, 30 July 2008 (CDT)

- You are right both notations are in this article for the same ket . But very often only
*J*and*M*are important and the small*j'*s aren't. Also in a different context the ket may have another origin than the coupling of two small*j*s (e.g., only one*j*or more than two*j*s). - The CG coefficients are sometimes written as
- but this notation is redundant in that the same two small
*j*s are given twice in one symbol.

- Some authors use indeed the term "Wigner coefficients", which historically is a much better name. But the majority of authors (especially the mathematically oriented authors) use Clebsch-Gordan for all sorts of groups, not just SO(3) and SU(2).

- About the Wiki flag: is it necessary to activate it for any edit? I thought that only the first time would be sufficient, because from the history of the article is then clear that it comes from WP.
- I'm melting away in my study right now, so I won't make any changes to this or any other article until the weather cools down.--Paul Wormer 08:27, 30 July 2008 (CDT)

- I made some small changes according to your replies. I'm pretty sure that the Wiki flag should be activated at every edit. This does more than putting a W in the history, it also puts a text at the bottom of the article, saying that parts come from Wikipedia. I couldn't find a clear statement about this, but CZ:How to convert Wikipedia articles to Citizendium articles says
*The "Content is from Wikipedia?" box is for the article as a whole, and not just the current edit.*

- and the (obsoleted) page CZ:The Big Cleanup says
*Check the "Content is from Wikipedia?" box if any part of the article is sourced from Wikipedia.*

- I made some small changes according to your replies. I'm pretty sure that the Wiki flag should be activated at every edit. This does more than putting a W in the history, it also puts a text at the bottom of the article, saying that parts come from Wikipedia. I couldn't find a clear statement about this, but CZ:How to convert Wikipedia articles to Citizendium articles says

- Finally, another question. The section on the orthogonality relations start with saying that these are most clearly written down by introducing the`alternative notation . But this is true by definition (using that the coefficients are real). I think stressing such a basic property of bra-ket notation may confuse people and it may be better to delete this sentence. -- Jitse Niesen 10:02, 2 August 2008 (CDT)
- Jitse, you are right again, but since not too many authors stress that a CG coefficient can be seen as an inner product, this remark has some use. Often (also by Wigner in his book) CG coefficients are introduced as elements of a matrix that, through a similarity transformation, reduces an outer product representation of a group. That is, it decomposes the representation matrices into block-diagonal matrices with irreducible blocks on the diagonal. This matrix is of course unitary since only orthonormal bases come into play. I always liked this inner product (bra-ket) character of the CG coefficient, and convinced my former colleague of the usefulness of this view. My former colleague (Gerrit Groenenboom) is the main author of the WP article. --Paul Wormer 10:35, 2 August 2008 (CDT)
- PS I looked at the WP history, and have to qualify: Gerrit Groenenboom is one of the main authors.--Paul Wormer 10:47, 2 August 2008 (CDT)

- Finally, another question. The section on the orthogonality relations start with saying that these are most clearly written down by introducing the`alternative notation . But this is true by definition (using that the coefficients are real). I think stressing such a basic property of bra-ket notation may confuse people and it may be better to delete this sentence. -- Jitse Niesen 10:02, 2 August 2008 (CDT)

- I see what you mean, yes. In that case, let's leave it as it is, at least until somebody has a better idea. -- Jitse Niesen 06:23, 3 August 2008 (CDT)

- Article with Definition
- Developing Articles
- Nonstub Articles
- Internal Articles
- Physics Developing Articles
- Physics Nonstub Articles
- Physics Internal Articles
- Mathematics Developing Articles
- Mathematics Nonstub Articles
- Mathematics Internal Articles
- Physics Underlinked Articles
- Underlinked Articles
- Mathematics Underlinked Articles