The product operator (PO) formalism is a widely accepted pictorial approach to describe the effect of a given NMR pulse sequence on weakly coupled spin systems. It is based in the decomposition of the density operator into a linear combination of products of spin angular momentum operators (83PROG163). For a two-spin system IS we can define 16 product operators:

• E is the unity operator
• I_x,y,z are the three x, y, and z components of I-spin magnetization
• S_x,y,z are the three x, y, and z components of S-spin magnetization
• 2I_x,yS_z are the two antiphase components of  transverse I-spin magnetization
• 2I_zS_x,y are the two antiphase components of  transverse S-spin magnetization
• 2I_zS_z is the longitudinal two-spin order component resulting of a specific disturbance of the normal Boltzman populations.
• 2I_x,yS_x,y are the two-spin coherence elements resulting of a superposition of zero-quantum and double-quantum coherences.

Basically, three effects can be independently considered in a NMR experiment:

• RF pulses
• Chemical shift evolution
• J coupling evolution.