Application of average Hamiltonian theory to the NMR of solids

The question of the validity of the average Hamiltonian theory is discussed. This is derived from consideration of the Floquet theorem for periodic systems. A perturbation scheme is developed and shown to give an average Hamiltonian equivalent to that obtained from the Magnus expansion. The convergence condition is shown to depend on the existence of resonances. These results are applied to a discussion of pulse spin-locking experiments.