This Demonstration illustrates the Clebsch–Gordan coefficients,

, which give the coupling amplitudes between uncoupled and coupled representations of two angular momenta

and

. In the

*uncoupled* representation, the

components of each angular momentum,

and

, are known; in the

*coupled* representation, the total (resultant) angular momentum

and its

component

are known. The Clebsch–Gordan coefficients are only nonzero when

and

; in the Demonstration we show these for

. The graphs give a vectorial representation of each

pair, showing the actual value together with all possible

values.