About: Racah W-coefficient

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Racah's W-coefficients were introduced by Giulio Racah in 1942. These coefficients have a purely mathematical definition. In physics they are used in calculations involving the quantum mechanical description of angular momentum, for example in atomic theory. Apart from a phase factor, Racah's W-coefficients are equal to Wigner's 6-j symbols, so any equation involving Racah's W-coefficients may be rewritten using 6-j symbols. This is often advantageous because the symmetry properties of 6-j symbols are easier to remember. Racah coefficients are related to recoupling coefficients by

Attributes	Values
rdf:type	Thing
rdfs:label	ラカー係数 (ja) Racah W-coefficient (en)
rdfs:comment	Racah's W-coefficients were introduced by Giulio Racah in 1942. These coefficients have a purely mathematical definition. In physics they are used in calculations involving the quantum mechanical description of angular momentum, for example in atomic theory. Apart from a phase factor, Racah's W-coefficients are equal to Wigner's 6-j symbols, so any equation involving Racah's W-coefficients may be rewritten using 6-j symbols. This is often advantageous because the symmetry properties of 6-j symbols are easier to remember. Racah coefficients are related to recoupling coefficients by (en)
foaf:depiction
dcterms:subject	Representation theory of Lie groups Rotational symmetry
Wikipage page ID	8924792 (xsd:integer)
Wikipage revision ID	1007127334 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Princeton University Press Quantum mechanics John Wiley & Sons Representation theory of Lie groups Clarendon Press Clebsch–Gordan coefficients Elsevier Giulio Racah Angular momentum 6-j symbol Addison-Wesley 3-j symbol Rotational symmetry Angular momentum coupling Pandya theorem Atomic theory Atomic orbital Unitary transformation Electron spin Scalar product Clebsch–Gordan coefficient
Link from a Wikipage to an external page	https://archive.org/details/angularmomentum0000brin https://archive.org/details/angularmomentumi0000edmo https://archive.org/details/in.ernet.dli.2015.212979
sameAs	Racah W-coefficient Racah W-coefficient Racah W-coefficient Racah W-coefficient
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thumbnail	wiki-commons:Special:FilePath/Racah_w_coefficient.svg?width=300
id	p/r110010 (en)
title	Racah-Wigner coefficients (en)
has abstract	Racah's W-coefficients were introduced by Giulio Racah in 1942. These coefficients have a purely mathematical definition. In physics they are used in calculations involving the quantum mechanical description of angular momentum, for example in atomic theory. The coefficients appear when there are three sources of angular momentum in the problem. For example, consider an atom with one electron in an s orbital and one electron in a p orbital. Each electron has electron spin angular momentum and in additionthe p orbital has orbital angular momentum (an s orbital has zero orbital angular momentum). The atom may be described by LS coupling or by jj coupling as explained in the article on angular momentum coupling. The transformation between the wave functions that correspond to these two couplings involves a Racah W-coefficient. Apart from a phase factor, Racah's W-coefficients are equal to Wigner's 6-j symbols, so any equation involving Racah's W-coefficients may be rewritten using 6-j symbols. This is often advantageous because the symmetry properties of 6-j symbols are easier to remember. Racah coefficients are related to recoupling coefficients by Recoupling coefficients are elements of a unitary transformation and their definition is given in the next section. Racah coefficients have more convenient symmetry properties than the recoupling coefficients (but less convenient than the 6-j symbols). (en)
prov:wasDerivedFrom	wikipedia-en:Racah_W-coefficient?oldid=1007127334&ns=0
page length (characters) of wiki page	8362 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Racah_W-coefficient
is Link from a Wikipage to another Wikipage of	Clebsch–Gordan coefficients Clebsch–Gordan coefficients for SU(3) Giulio Racah 6-j symbol 9-j symbol Pandya theorem August 1965 Racah's W-coefficient
is Wikipage redirect of	Racah's W-coefficient
is foaf:primaryTopic of	wikipedia-en:Racah_W-coefficient

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