Projection of Angular Momentum on Basis Sets

A matrix representation of Hamiltonian H is given by eq. (1) assxuning eigenfunction matrix (p and eigenvalue matrix A  

Here Xp, X, and X are nondegenerate eigenvalues. Among matriees Ep, E, and Ey, the following relation exists  

Eaeh of the terms appearing in eq. (6) is defined as a projeetion matrix onto a basis set. Thus, eaeh term ( ) -Ej (J p,q,r) is defined as follows  

---