Introduction to Spin, Magnetic Resonance and Polarization

Abstract

In this chapter, we shall review the mathematical formalism required for the understanding of the spin physics of polarized targets. Particular focus is given to the problems treating the situations that are favorable for obtaining high polarizations: high magnetic field and low lattice temperature. In the following sections we shall first discuss the concept of the spin and magnetic moment and work out in detail some standard quantum mechanical problems involving these variables. The quantum statistics of a system of spins is then overviewed, before briefly introducing the thermodynamics of spin systems. Most of these can be found in well-known textbooks of quantum mechanics, such as those of Dicke and Wittke [1] and of Landau and Lifshitz [2], and of magnetic resonance, such as Abragam [3], Goldman [4], Abragam and Goldman [5] and Slichter [6]. The main justification for presenting textbook material is that we need to make frequent reference to this basic formalism. Three further reasons are: