  The addition of angular momenta can be reduced to elementary coupling
processes of spin-$\frac{1}{2}$-particles. In this way, a method is developed
which allows for a non-recursive, simultaneous computation of all
Clebsch-Gordan coefficients concerning the addition of two angular momenta. The
relevant equations can be interpreted easily, analogously to simple
probabilistic considerations. They provide an improved understanding of the
addition of angular momenta as well as a practicable evaluation of
Clebsch-Gordan coefficients in an easier way than within the well-known
methods.
