Fer expansion for effective propagators and Hamiltonians in NMR

Solving a time-dependent linear differential equation towards obtaining propagators is a central problem to NMR in general and solid-state NMR in particular. Designing of various pulse sequences and understanding of different experiments are based on the form of effective Hamiltonians and/or effective propagators. The commonly used methods for this are average Hamiltonian theory based on Magnus expansion and Floquet theory where use of van Vleck perturbation is employed. Here, we dwell upon an alternative expansion method to solving time-dependent linear differential equations called Fer expansion. We highlight the basics of this scheme and hint at its potential by considering Bloch-Siegert shift and heteronuclear dipolar decoupling in solid-state NMR.