 These facts can be used to devise an effective storage scheme.A system of two angular momenta with magnitudes and can be described either in terms of the uncoupled basis states (labeled by the quantum numbers and ), or the coupled basis states (labeled by and ).The 3-"j" symbols constitute a unitary transformation between these two bases, and this unitarity implies the orthogonality relations
The "triangular delta" is equal to 1 when the triad ("j"1, "j"2, "j"3) satisfies the triangle conditions, and is zero otherwise.