Magnetization density calculation for diffusing spins

The evolution operator method is used to describe diffusion of nuclear-spin magnetization in a gradient polarizing magnetic field during a NMR pulse experiment. The transversal magnetization density evolution in an unrestricted liquid is determined by the received Green function. The behavior of initially inhomogeneous magnetization under the influence of the applied pulse sequences is obtained. Additionally the evolution operator was successfully applied to the diffusion process in bounded volumes. The transversal magnetization density for the restricted diffusion was determined. The achieved results are in good accordance to the well-known formulas for NMR echo amplitudes determined with other theoretical methods.