The Effect of RF Pulses on Product Operators

This is pretty complicated, but the advantage is that we can keep track of everything of importance. Any pulse sequence can, in principle, be examined to see what effect it will have on the sample magnetization and what observable signals will remain at the end. Product operator formalism represents the full quantum-mechanical phenomenon of NMR, so that any type of experiment including mysterious things like multiple-quantum coherences (MQCs) can be represented correctly. 

The effect of pulses is very simple each individual operator is acted on by the pulse, and replaced by the result of that rotation about the Bi vector. For example, consider the effect of a 90° XH pulse on the x axis  

These are exactly the same as the vector rotations, and you should draw a small set of coordinate axes in the margin of your paper to figure out these rotations as you work with product operators (Fig. 7.12). Note that 13C net magnetization is not affected by a XH pulse (S-y - Sy). The effect of a 90° 13C pulse on the y axis is likewise the same as the vector model predicts  

For two-spin operators, just figure out the effect of the pulse on each of the operators and replace the each starting operator with the result of the rotation. For example, for a 180° 13 C pulse on the x axis 

2IySz - 2I-y(—Sz) = —21ySz (only Sz is affected by the13C pulse) 

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