Article

Journal of Mathematical Chemistry

, Volume 26, Issue 1, pp 15-26

On the role of reachability and observability in NMR experimentation

  • Raimund J. OberAffiliated withCenter for Engineering Mathematics, University of Texas at DallasCancer Immunobiology Center and Center for Immunology, University of Texas Southwestern Medical Center
  • , Viswanath RamakrishnaAffiliated withCenter for Engineering Mathematics, University of Texas at Dallas
  • , E. Sally WardAffiliated withCancer Immunobiology Center and Center for Immunology, University of Texas Southwestern Medical Center

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Abstract

It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered.