The Use of Clebsch Gordan Coefficients in Analysis of Spin- Spin Interaction under Nuclear Magnetic Resonance

In nuclear magnetic resonance we have that [H, Fz] = 0 and thus H and Fz have a common set of orthonormalized eigenfunctions that employ the use of Clebsch-_Gordan coefficients that we use in the present paper. We have calculated the Clebsch_Gordan coefficients with the value j1xj2 =1/2x1/2 and we estimated the energy levels and the transition energies of this system under the nuclear magnetic resonance. The generalities of the A2 , AB; AX, and three spin system are studied.