Abstract
A simple technique for solving the Torrey–Bloch equations appearing in the calculation of the NMR signal under gradient fields is presented. It is applicable to arbitrary time dependence of the gradient field to arbitrary initial distribution of spins, and to spin motion on discrete lattices as well as in the continuum under conditions of unrestricted diffusion. Known results are recovered as particular cases and new results are presented. The discrete lattice results are shown to be similar to known results for restricted diffusion in the continuum. Also presented is a surprising equivalence between results for a simple two-site hopping model and earlier expressions for the NMR signal for spins undergoing restricted diffusion in a continuum.
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