Abstract
Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations that continues today. Much progress has been made in the utilization of solid-state NMR to illuminate molecular structure and dynamics in systems not controllable by any other way. NMR deals with time-dependent perturbations of nuclear spin systems and solving the time-dependent Schrodinger equation is a central problem in quantum physics in general and solid-state NMR in particular. This theoretical perspective outlines the methods used to treat theoretical problems in solid-state NMR as well as the recent theoretical development of spin dynamics in NMR and physics. The purpose of this review is to unravel the versatility of theories in solid-state NMR and to present the recent theoretical developments of spin dynamics.
Highlights
Methods developed over the past decade have enabled us to make a significant progress in the area of solid-state nuclear magnetic resonance (NMR) by introducing an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state NMR in particular [9] [11] [24]
The FME approach is an alternative approach recently developed by Casas and co-workers to solve time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (SSNMR) in particular [24]
Our descriptions for all four theories suggest that the Fer expansion is advantageous over the other three theories (AHT, Floquet theory (FLT), and FME) in calculation of higher-order corrections
Summary
Methods developed over the past decade have enabled us to make a significant progress in the area of solid-state NMR by introducing an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state NMR in particular [9] [11] [24]. The Fer expansion was formulated by Fer and later revised by Fer [29], Klarsfeld and Oteo [31], Casas et al [32], and Blanes et al [33] This expansion employs the form of a product of sub-propagators, which appears to be suitable for examination of time-dependence of the density matrix for each average Hamiltonian at different orders. Some papers which outline the comparison of both theories (FME and FE) in NMR and physics were recently published in the solid-state NMR, chemical physics, and physics [34] [35]
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