Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.
Below, this definition is made precise by defining angular momentum operators, angular momentum eigenstates, and tensor products of these states.
From the formal definition of angular momentum, recursion relations for the Clebsch–Gordan coefficients can be found. To find numerical values for the coefficients a phase convention must be adopted. Below the Condon–Shortley phase convention is chosen.
Read more about Clebsch–Gordan Coefficients: Angular Momentum Operators, Angular Momentum States, Tensor Product Space, Formal Definition of Clebsch–Gordan Coefficients, Recursion Relations, Explicit Expression, Orthogonality Relations, Special Cases, Symmetry Properties, Relation To 3-jm Symbols, Relation To Wigner D-matrices, Other Properties, SU(N) Clebsch–Gordan Coefficients