Product operator formalism

Yuning Zhang, Fei Han, Alexej Jerschow

Research output: Contribution to journalArticlepeer-review


The product operator formalism provides a convenient and powerful framework for analyzing NMR pulse sequences. Its appeal arises from the ability to bridge the gap between the classical vector picture and the density matrix formalism. Once product operator rules are established, it is possible to analyze pulse sequences without any knowledge of quantum mechanics, while retaining the intuitive appeal of the classical vector model. It works best for a collection of spin 1/2 nuclei with weak J-coupling. The operator rules, and their applications to several simple sequences are reviewed here.

Original languageEnglish (US)
Pages (from-to)229-235
Number of pages7
Issue number2
StatePublished - 2013


  • COSY
  • Density matrix
  • HSQC
  • J-coupling
  • Product operator formalism
  • Spin echoes

ASJC Scopus subject areas

  • Analytical Chemistry
  • Biochemistry
  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Spectroscopy


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