Section 5.1 Introduction
In the previous chapters, we have emphasized the use of the wavefunction \(\psi(x)\) to describe the quantum state of a particle. This wavefunction formalism is mainly focused on answering the question “Where is the particle?” by virtue of the fact that the square of the magnitude of the wavefunction, \(\left| \psi(x) \right|^2\text{,}\) represents the probability density for finding the particle near the location \(x\text{.}\) This wavefunction approach is useful in describing how electrons arrange themselves in an individual atom as well as describing how electrons behave in a conductor, among other things. On the other hand, there are certain systems for which the wavefunction approach is neither appropriate nor meaningful, as for example the quantum description of photon states and, as we shall see later in this chapter, the quantum description of spin. Therefore in this chapter we will develop a more abstract mathematical structure in which to describe quantum systems that is more widely applicable and also reveals more of the non-intuitive quantum behavior. We will use this new mathematical formalism to describe a property of elementary particles called spin angular momentum, or simply spin, and how the spin of the particle interacts with a magnetic field. This description has important implications for understanding nuclear magnetic resonance (NMR) which is the basis for magnetic resonance imaging (MRI).