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Clebsch–Gordan coefficients
In
physics
, the
Clebsch–Gordan (CG) coefficients
are numbers that arise in
angular momentum coupling
in
quantum mechanics
. They appear as the expansion coefficients of
total angular momentum
eigenstates
in an uncoupled
tensor product
basis. 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
and
Paul Gordan
, who encountered an equivalent problem in
invariant theory
.
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