Coeficientes Clebsch—Gordan

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Coeficientes Clebsch—Gordan

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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.

English Wikipedia http://en.wikipedia.org/wiki/Clebsch?Gordan_coefficients

Spanish wikipedia http://es.wikipedia.org/wiki/Coeficientes_Clebsch?Gordan

Wiki page external link http://www.volya.net/vc http://pdg.lbl.gov/2011/reviews/rpp2011-rev-clebsch-gordan-coefs.pdf http://phys.csuchico.edu/C-G/ http://homepages.physik.uni-muenchen.de/~vondelft/Papers/ClebschGordan/