B Transition probabilities in the xy plane

In calculating longitudinal relaxation, we started from four eigenstates ---), 

However, here ara) afi) f5ct) fifi) are not eigenstates of the energy. Nevertheless, they are still orthogonal and can always be expanded in eigenvectors of the energy. For example, in the present case of spin 1/2 we have  

This equation is analogous to Eq. (V.2), and through a procedure analogous to that already reported, the equations for T x in the like-spin case (Eq. (3.12)) and unlike-spin case (Eq. (3.17)) are obtained. 

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