Simple Solutions of the Torrey–Bloch Equations in the NMR Study of Molecular Diffusion

A simple technique for solving the Torrey–Bloch equations apin unconfined geometry. We obtain an expression for the pearing in the calculation of the NMR signal under gradient fields signal which contains explicit information about the initial is presented. It is applicable to arbitrary time dependence of the distribution of spins and show that it reduces to well-known gradient field to arbitrary initial distribution of spins, and to spin expressions in particular cases. For instance, we show that motion on discrete lattices as well as in the continuum under the contribution of the initial spin distribution factor cancels conditions of unrestricted diffusion. Known results are recovered for a bipolar pulse experiment such as the usual Stejskal– as particular cases and new results are presented. The discrete Tanner diffusion experiment. We apply our result to relalattice results are shown to be similar to known results for retively new situations such as a slow turn-on of the gradient, stricted diffusion in the continuum. Also presented is a surprising sinusoidal gradient, and also calculate the time dependence equivalence between results for a simple two-site hopping model of the signal that would arise in nonstandard experiments and earlier expressions for the NMR signal for spins undergoing restricted diffusion in a continuum. q 1997 Academic Press which would be sensitive to nonuniform initial magnetization density such as the Gaussian and the square distribution. We give a generalization of our transformation technique to spin motion in discrete space as among Wannier states in a