Talk:Wigner–Eckart theorem

I think we need an article about the Wigner-Eckart theorem!

Here are some links: Link 1 Link 2

-spiralhighway

it reads "where (T) is a rank q spherical tensor", shouldn't it be a rank k spherical tensor?

---> According to the reference article: http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/TensorOperators.htm

    the subscript is the rank and superscript is the component. It looks like the example was worked out wrong, so I corrected it
    bphillab 14:33, 21 January 2007 (UTC)[reply]

Sorry, no. The rank is the superscript. $T_{q}^{k}$ is rank k, component q. Looking at the CG coefficient, it'd have to be that way; k is analogous to j, and q is analogous to m. Therefore k is the one that determines the overall properties (the rank) and q is less important. JFlav (talk) 05:35, 27 February 2008 (UTC)[reply]

I think that this article is quite confusing given there is no page on spherical tensors. Should spherical tensors be defined on this page?h

i think one should keep up the same notation all over the article now it is very confusing:

the first definition is:

$\langle jm|T_{q}^{k}|j'm'\rangle =\langle j||T^{k}||j'\rangle C_{kqj'm'}^{jm}$

in the example it should therefore read:

\langle njm|x|n'j'm'\rangle ={\frac {1}{\sqrt {2}}}\langle nj||T^{1}||n'j'\rangle (C_{1(-1)j'm'}^{jm}-C_{11j'm'}^{jm})

but up to now it reads:

\langle njm|x|njm\rangle ={\frac {1}{\sqrt {2}}}\langle nj||T^{1}||nj\rangle (C_{jm11}^{jm}-C_{jm1(-1)}^{jm})

i think that should be changed otherwise it is extremly confusing. i will do this if I'm wrong please correct me —Preceding unsigned comment added by 141.84.136.26 (talk) 15:18, 18 January 2011 (UTC)[reply]

Sakurai 1993, p. 239, f. 3.10.31 defines Wigner-Eckart theorem with the reduced matrix element normalized by a factor of 1/sqrt(2j+1). T(k) does not change for different j's, but this factor does. Tormondo (talk) 11:24, 18 March 2012 (UTC)[reply]

What is q?

Shouldn't the article mention the definition of q? Does it indicate an element of tensor T? An explanation about spherical tensors is needed in this article. — Preceding unsigned comment added by 128.178.54.250 (talk) 13:47, 25 April 2012 (UTC)[reply]

Assessment comment

The comment(s) below were originally left at Talk:Wigner–Eckart theorem/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

In physics the 'k' conventionally refers to the rank of the tensor and 'q' to the component. Both Sakurai (Modern Quantum Mech) and Messiah (Quantum Mechanics, vol II) place the k in the upper index and q lower. Shankar (Principles of Quantum) switches the index placement (k - rank, on bottom; q - component, on top).

So, either index placement should be ok, but its probably not a good idea to differ from the conventional letters used.

Rephorm (talk) 15:22, 15 February 2008 (UTC)[reply]

Substituted at 22:06, 26 June 2016 (UTC)