Formalisms for the description of multiple-pulse NMR experiments

During the last few years, the product operator formalism has provided the most popular theoretical basis for the description and analysis of multiple-pulse NMR experiments, having all but replaced the more cumbersome density matrix method. However, those unacquainted with the detailed theory behind the formalism experience difficulty in arriving at a working understanding of the method. In this paper an introductory treatment of the theory for spin- 1 2 systems with weak coupling using results from both the product operator and density matrix approaches is provided. Based on a handful of results from quantum mechanics and matrix algebra a small number of physical ideas are introduced which allow description of the evolution of product operators during any multiple-pulse experiment. These ideas are illustrated with an analysis of a COSY experiment.