Theoretical background of magnetic resonance

By the middle of the 1920's the famous experiment performed by W. Gerlach and O. Stern made it clear that the electron has an intrinsic angular momentum referred to as spin. Following this concept, Rabi and his coworkers continued the research on the spin of the proton and its interaction with a magnetic field in the 1930's. With their results given in 1946, Purcell and Bloch succesfully measured the effect of precession of the spins around a magnetic field and also explained the theoretical background of this phenomenon. The contribution of these early results to modern MRI technology is unquestionable: without the understanding of the physics of nuclear magnetic resonance, its application to biomedical imaging would be impossible.

In the following the basic principles of spin precession and excitation is presented followed by the concept of relaxation and spin echo. These processes can be described in two ways: using classical magnetic moments or quantum mechanics. It can be shown that the two approaches lead to equivalent results, i.e. the mean value of the quantum mechanical quantities are the same as come from the classical description. In these notes the equivalence will be shown solely for the precession, beyond that the classical way is presented because of its far more intuitive and graphic nature.