Wigner 3j symbols

E674699

angular momentum coupling coefficient mathematical object special function tensor coupling coefficient

Wigner 3j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling and recoupling of three angular momenta with well-defined symmetry properties.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form	Occurrences
Wigner 6j symbols	1

Statements (48)

Predicate	Object
instanceOf	angular momentum coupling coefficient ⓘ mathematical object ⓘ special function ⓘ tensor coupling coefficient ⓘ
appearsIn	Gaunt coefficients NERFINISHED ⓘ addition of spherical harmonics ⓘ evaluation of matrix elements of tensor operators ⓘ multipole expansion of interactions ⓘ spherical tensor operator theory ⓘ
belongsTo	representation theory of SU(2) ⓘ theory of angular momentum in quantum mechanics ⓘ
definedOver	half-integer and integer angular momentum quantum numbers ⓘ
expressibleInTermsOf	Clebsch–Gordan coefficients NERFINISHED ⓘ
hasAlternativeFormulation	group-theoretical coupling coefficients of SU(2) ⓘ integrals of three spherical harmonics ⓘ
hasComputationalUse	numerical evaluation of transition amplitudes ⓘ symbolic manipulation in computer algebra systems ⓘ tabulation of angular momentum coupling coefficients ⓘ
hasNotation	( j1 j2 j3 ; m1 m2 m3 ) with 3x2 array brackets ⓘ
hasProperty	completeness relations ⓘ orthogonality relations ⓘ real values in standard phase convention ⓘ vanish when m quantum numbers do not sum to zero ⓘ vanish when triangle inequalities are violated ⓘ well-defined phase convention ⓘ
hasSelectionRule	j1 j2 j3 satisfy angular momentum addition rules ⓘ m1 plus m2 plus m3 equals zero ⓘ parity condition j1 plus j2 plus j3 integer ⓘ triangle condition for j1 j2 j3 ⓘ
hasSymmetryProperty	invariance under even permutations of columns ⓘ phase factor under column permutations ⓘ sign change under odd permutations of columns ⓘ
namedAfter	Eugene Wigner NERFINISHED ⓘ
relatedTo	Clebsch–Gordan coefficients NERFINISHED ⓘ Racah coefficients NERFINISHED ⓘ Wigner 6j symbols ⓘ Wigner 9j symbols NERFINISHED ⓘ
standardReference	Angular Momentum in Quantum Mechanics by A. R. Edmonds NERFINISHED ⓘ Quantum Theory of Angular Momentum by D. A. Varshalovich et al. NERFINISHED ⓘ
usedFor	coupling of three angular momenta ⓘ evaluation of Clebsch–Gordan coefficient symmetries ⓘ recoupling of angular momenta ⓘ
usedIn	angular momentum theory ⓘ atomic physics ⓘ molecular spectroscopy ⓘ nuclear physics ⓘ quantum chemistry ⓘ quantum mechanics ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Condon–Shortley phase → relatedTo → Wigner 3j symbols ⓘ

Clebsch–Gordan coefficients → relatedTo → Wigner 3j symbols ⓘ

this entity surface form: Wigner 6j symbols