Abstract
Density matrix calculations are very powerful but also very time-consuming and error-prone when done by hand. The product operator formalism provides a compact way of doing “back-of-the-envelope” density matrix operations. In order to contrast the density operator method with the product operator method and to make clear the genesis of the product operator formalism a short discussion of a density matrix calculation is performed. The Cartesian product operator method is then presented and the rules for its use are developed. Multiple quantum coherence is defined and its genesis and evolution in time are explored. Helpful visualisations of product operator evolutions are presented as rotation diagrams. Several NMR pulse sequences are analysed and a visual operator-tree approach to analysis is presented. Single-transition product operators are discussed in preparation for the treatment of coherence transfer and relaxation.
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