An efficient quantum-mechanical approach is presented for the mechanical treatment is necessary for an accurate description computation of the short-term propagation of nuclear polarization of spin-propagation processes, since it has been demonin many-spin systems, known as spin diffusion, which carries strated also experimentally that for short evolution times 1 H structural information. It is based on the fact that for short time spin diffusion is indeed a deterministic, reversible process intervals the spin evolution under dipolar coupling can be ex- (12). An exact quantum-mechanical treatment of N dipolarpressed analytically by rotations in three-and four-dimensional coupled spins-1 2 involves propagator matrices in the zerosubspaces of the Liouville space. Due to its high computational efficiency, the approach allows the treatment of several dozens of quantum space of the dimension ͫ 2N N ͬ (9), which renders coupled spins and is well suited to the rapid calculation of spin propagation in oriented samples and in powders. ᭧ 1997 Academic calculations even for small systems with N ú 10 prohibi-Press tively expensive. It has been realized from the very beginning that important aspects of spin propagation can also be described with sim-