The dynamics of spin is one of the most important problems in Modern Physics, and its study granted the Nobel Prize in Physics to several important scientists of the 20th century, the names of Rabi, Bloch and Purcell being worth mentioning. However, given the mathematical complexity associated with the problem of spin ½, whose understanding requires at least rudimentary knowledge of group theory and rotation group representation, it is not normally approached within depth in undergraduate courses. This way, the present work intends to fill this gap through the concise and self-contained presentation of the tools necessary to understand the dynamics of spin and its practical applications. Whenever possible, the most important historical events are mentioned. The fundamental postulates of quantum mechanics and the rotation group theory are presented in a sufficient depth to allow the understanding of the main concepts associated with spin. Bloch’s equations, not including dissipative effects, essential for understanding nuclear magnetic resonance (NMR) are presented from first principles, and solved in the case of the rotating frame of reference.
Keywords
Magnetic resonance; spin dynamic; Bloch equation; rotation operation
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