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Solid-State NMR by Paul Hodgkinson, Robin K. Harris, David C. Apperley

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APPENDIX C

LIOUVILLE SPACE, RELAXATION & EXCHANGE

C.1 INTRODUCTION TO LIOUVILLE SPACE

There are a number of important processes that cannot be described in terms of the evolution of a density operator under a Hamiltonian, as given by the Liouville–von Neumann equation (equation 4.50). The most important of these are relaxation of the nuclear spin coherences and chemical exchange. The reason why they cannot be accounted for in the nuclear spin Hamiltonian is their dependence on the external degrees of freedom that were discarded in reducing the total system Hamiltonian to one involving just the nuclear spins, as discussed in section 4.1. NMR relaxation, for instance, is driven by molecular motion, while the derivation of the nuclear spin Hamiltonian ...

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