Abstract
This article reviews theoretical approaches for controlling spin dynamics in solid-state nuclear magnetic resonance. We present fundamental theories in the history of NMR, namely, the average Hamiltonian and Floquet theories. We also discuss emerging theories such as the Fer and Floquet-Magnus expansions. These theories allow one to solve the time-dependent Schrodinger equation, which is still the central problem in spin dynamics of solid-state NMR. Examples from the literature that highlight several applications of these theories are presented, and particular attention is paid to numerical integrators and propagator operators. The problem of time propagation calculated with Chebychev expansion and the future development of numerical directions with the Cayley transformation are considered. The bibliography includes 190 references.
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