Vector Coupling Calculator

Clebsch-Gordan coefficient

C =

C JMj1 m1, j2 m2  often also denoted as <j1 m1, j2 m2|j1 j2 J M> and referred to as vector-coupling or Wigner coefficient. The calculation uses the phase convention [1,2], where <j1 j1, j2 m2|j1 j2 J J> is positive for all allowed J (m2=J-j1)  

Three-j Symbol


( ) =

The Wigner 3-j symbol is a more symmetric expression of the vector coupling, directly related to the Clebsch-Gordan coefficient. For symmetry property and other relations see [1].

Six-j Symbol

{ } =