Liouvillians in NMR: The direct method revisited

► We provide a complete and exact way of evolving the density matrix in NMR. ► This gives us a systematic way of calculating what goes on in any pulse NMR experiment. ► The method is based on a number of results from the quantum theory of angular momentum. ► Very little information on the wavefunctions, the operators that act on them, and their commutation properties is needed. ► Explicit formulae are presented for all the common NMR interactions: Zeeman, RF, scalar and dipolar coupling and quadrupolar interaction.