Abstract: For an NMR (nuclear magnetic resonance) experiment exact quantum-mechanical solutions have been obtained for the effect of RF (radiofrequency) pulses of constant amplitude, phase, and frequency, on any initial configuration of an ImSn J-coupled system. Subsets of these equations (rotation matrices) can be used to calculate the exact result of shaped RF pulses (modulated amplitude and phase). The rotation matrices remain valid when no RF is applied, so the result of a pulse sequence can be calculated continuosly throughout an NMR pulse sequence, yielding a method useful for specifying steps throughout sequences, the design of new sequences, or the display or debugging of sequences. During continuous wave (CW) decoupling applied to the I spins, the S-spin signal yields sidebands whose frequency depends on RF field strength and homogeneity, and these sidebands are further enhanced starting with antiparallel spinstates instead of in-phase magnetization.