Symbolic NMR product operator calculations



Symbolic nuclear magnetic resonance (NMR) product operator calculations provide an analytic, intuitive, yet precise description of the time evolution of the density operator during an NMR experiment. NMR experiments are implemented as pulse sequences consisting of short radiofrequency pulses separated by delay periods during which the spin system evolves under the influence of the static external magnetic field and spin–spin interactions. The quantum mechanical calculations to follow the time evolution of the density operator can be decomposed into the repeated application of a set of simple rules, known as the product operator formalism, that naturally lend themselves to symbolic computation. This article describes a complete implementation of the NMR Product Operator formalism in MAthematica (POMA), which has greatly simplified the development of many NMR pulse sequences, and provided insight into their functioning. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006