Abstract
An equation of motion is derived for the reduced density matrix of a system of spins coupled to a second system of spins strongly relaxing on account of their coupling to a thermal reservoir. The symmetry and other general properties of this equation are discussed. The applications of the equation are considered in relation to the problem of calculating the high resolution nuclear magnetic resonance band shape of a group of spin - 1/2 nuclei scalar coupled to a group of nuclei of spin > 1/2 which are relaxing via the quadrupolar mechanism. Explicit formulae are derived for some simple examples of such spin systems.