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- Clebsch–Gordan_coefficients abstract "In physics, the Clebsch–Gordan coefficients are sets of numbers that arise in angular momentum coupling under the laws of quantum mechanics.In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly. The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory.In terms of classical mathematics, the CG coefficients, or at least those associated to the group SO(3), may be defined much more directly, by means of formulae for the multiplication of spherical harmonics. The addition of spins in quantum-mechanical terms can be read directly from this approach. The formulas below use Dirac's bra–ket notation.Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.Below, this definition is made precise by defining angular momentum operators, angular momentum eigenstates, and tensor products of these states.From the formal definition of angular momentum, recursion relations for the Clebsch–Gordan coefficients can be found. To find numerical values for the coefficients a phase convention must be adopted. Below the Condon–Shortley phase convention is chosen.".
- Clebsch–Gordan_coefficients wikiPageID "1074990".
- Clebsch–Gordan_coefficients wikiPageRevisionID "599759310".
- Clebsch–Gordan_coefficients subject Category:Quantum_mechanics.
- Clebsch–Gordan_coefficients subject Category:Representation_theory_of_Lie_groups.
- Clebsch–Gordan_coefficients subject Category:Rotation_in_three_dimensions.
- Clebsch–Gordan_coefficients subject Category:Rotational_symmetry.
- Clebsch–Gordan_coefficients comment "In physics, the Clebsch–Gordan coefficients are sets of numbers that arise in angular momentum coupling under the laws of quantum mechanics.In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly.".
- Clebsch–Gordan_coefficients label "Clebsch-Gordan-Koeffizient".
- Clebsch–Gordan_coefficients label "Clebsch-Gordan-coëfficienten".
- Clebsch–Gordan_coefficients label "Clebsch–Gordan coefficients".
- Clebsch–Gordan_coefficients label "Coefficienti di Clebsch-Gordan".
- Clebsch–Gordan_coefficients label "Coefficients de Clebsch-Gordan".
- Clebsch–Gordan_coefficients label "Coeficientes Clebsch—Gordan".
- Clebsch–Gordan_coefficients label "Коэффициенты Клебша — Гордана".
- Clebsch–Gordan_coefficients label "クレブシュ-ゴルダン係数".
- Clebsch–Gordan_coefficients sameAs Clebsch%E2%80%93Gordan_coefficients.
- Clebsch–Gordan_coefficients sameAs Clebsch-Gordan-Koeffizient.
- Clebsch–Gordan_coefficients sameAs Coeficientes_Clebsch—Gordan.
- Clebsch–Gordan_coefficients sameAs Coefficients_de_Clebsch-Gordan.
- Clebsch–Gordan_coefficients sameAs Coefficienti_di_Clebsch-Gordan.
- Clebsch–Gordan_coefficients sameAs クレブシュ-ゴルダン係数.
- Clebsch–Gordan_coefficients sameAs 클렙슈-고르단_계수.
- Clebsch–Gordan_coefficients sameAs Clebsch-Gordan-coëfficienten.
- Clebsch–Gordan_coefficients sameAs Q898619.
- Clebsch–Gordan_coefficients sameAs Q898619.
- Clebsch–Gordan_coefficients wasDerivedFrom Clebsch–Gordan_coefficients?oldid=599759310.