The Floquet–Magnus and Fer Expansions: Application to Control the Spin Dynamics During the Phase Modulated Lee–Goldburg Radiation in Solid-State NMR

Floquet–Magnus and Fer expansion (FE) schemes are used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators. This work focuses on applying the Floquet–Magnus and FE approaches to control the spin system evolution during the phase modulate Lee–Goldburg radiation experiment. Until now, the Frequency switched Lee–Goldburg and its variant called the Phase module Lee–Goldburg have been treated by only the average Hamiltonian theory and the bimodal Floquet approach. In this paper, we use the two developing expansion schemes in solid-state NMR for the calculation of the effective Hamiltonian and propagator during the spin dynamics. Our work unifies and generalizes existing results of the Floquet–Magnus and FEs and delivers illustrations of novel springs that boost previous applications that are based on the classical information. The generality of this work points to potential applications in problems related to solid-state NMR and theoretical developments of spectroscopy as well as interdisciplinary research areas whenever they include spin dynamics concepts.