V. VARIOUS OPERATOR FORMALISMS FOR THE DESCRIPTION OF PULSE METHODS IN NMR Geoffrey BODENHAUSEN Institut de Chimie Organique Universite de Lausanne Rue de Ia Barre 2 CH-1005 Lausanne Switzerland ABSTRACT. A brief survey of various operator formalisms is presented in order to provide some clues as to which type of theory is most suitable for the description of various experiments. 1. Introduction In recent years, much attention has been given to various operator formalisms designed to simplify the description of more or less sophisticated pulse experiments. It is often difficult to assess which formalism (if any) is needed to describe a given experimental situation. We have to consider the nature of the spin system as well as the type of experiment. In this context, spin systems differ in that they may be in isotropic or anisotropic phase, that they mayor may not have resolved couplings, possess magnetically equivalent subsets, etc. Experimental techniques differ in that they may merely employ pulses with flip angles of 90 0 and multiples thereof, or use arbitrary flip angles; in that they may include pulse sandwiches designed to induce composite rotations; in that they may incorporate the selection of coherence pathways by phase-cycling, etc. Apart from the well-known papers by S(.!Irensen et al.(l), van der Yen and Hilbers (2), and by Wright and Packer (3), the subject is extensively reviewed in Ernst's monograph (4). A lucid recapitulation, entitled "density-operator theory of pulses and precession", was written by Levitt some years ago and published only recently (5). Some recent extensions using products of tensor operators to describe equivalent protons in methyl groups have been published by Muller et al. (6), while Jaccard et al. (7) have applied similar concepts to S = 3/2 spins. The description of strongly coupled systems with the help of operator products (rather than the usual density matrix representations) has been addressed very recently by Kay and McClung (8). A useful compilation of matrix representations of operator products is contained in the appendix of Chandrakumar and Subramanian's book (9), who also give many non-trivial examples of operator treatments. The volume by Gerstein and Dybowski (to) also contains many enlightening chapters on operators. 51 P. Granger and R. K. Harris (eds.) Multinuclear Magnetic Resonance in Liquids and Solids - Chemical Applications, 51-61. © 1990 Kluwer Academic Publishers.