One frequently recurring example of coalgebras occurs in representation theory, and in particular, in the representation theory of the rotation group. A primary task, of practical use in physics, is to obtain combinations of systems with different states of angular momentum and spin. For this purpose, one uses the Clebsch–Gordan coefficients. Given two systems formula_1 with angular momenta formula_2 and formula_3, a particularly important task is to find the total angular momentum formula_4 given the combined state formula_5. This is provided by the total angular momentum operator, which extracts the needed quantity from each side of the tensor product. It can be written as an "external" tensor product