A General Graphical Method for Angular Momentum

A graphical method is presented allowing the representations of $``j-m\text{'}\text{'}$ and $``3nj\text{'}\text{'}$ coefficients, spherical harmonics, irreducible tensor operators, and rotation matrices. Rules are established which permit calculations on expressions with the above elements. As the main difficulty of using $``3j\text{'}\text{'}$ Wigner coefficients is the construction of the phase, an algorithm is proposed which simplifies this problem. Concrete examples are given for this general method.