Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.