The Ups and Downs of Classical and Quantum Formulations of Magnetic Resonance

This chapter describes typical misunderstandings frequently encountered in introductions to nuclear magnetic resonance (NMR), for example, as used for chemical analysis and for magnetic resonance imaging (MRI). It is aimed at those users who are familiar with the basics but have an interest in the connection between the seemingly very different classical and quantum descriptions. Such understanding is needed by students, authors, and lecturers, in particular. With limited complexity, the text introduces probabilistic classical and quantum mechanics with emphasis on similarities and differences. It describes important concepts and the roles of measurement, eigenstates, superpositions, entanglement, and interference, all discussed with reference to spin dynamics for both isolated nuclei and ensembles. The dynamics of basic NMR are shown to be similar to those of coupled oscillators (e.g., pendulums), which gives insight into the resonance phenomenon itself as well as spectral features resulting from intramolecular J-coupling of atomic nuclei. It is discussed how classical and quantum mechanics give rise to similar expectations for basic NMR and why a classical understanding is central.