The properties of angular momentum and its connection to magnetic moment are explored, based on a reconsideration of the Stern-Gerlach experiment and gauge invariance. The separation of angular momentum of a quantum system of particles into orbital angular momentum plus intrinsic angular momentum is reconsidered, within the limits of the Schrödinger theory. A proof is given that, for systems of more than two particles, unless all of them have the same mass, the possibility of having eigenvalues of the form
(n+1/2)ℏ is not excluded for the operators of angular momentum of the centre of mass and the internal angular momentum. \noindent\textbf{PACS: 03.65.Ta} angular momentum, magnetic moment, spin crisis
In this chapter we shall treat two of the most important observables of quantum mechanical systems: angular momentum and spin. We shall argue that angular momentum is the generator of rotations. In quantummechanics, angular momentum is quantized in units of the reduced Planck constant. The quantization of angular momentum is dealt with by finding the angular momentum eigenvalues and eigenstates. We shall then apply the theory of angular momentum to study the hydrogen atom. Spin is an intrinsic angular momentum of subatomic particles and therefore corresponds to an important intrinsic degree of freedom. We shall discuss briefly how spin was discovered and many of its important properties. Finally, we shall also explore here some further subtleties of quantum theory.a When we consider quantum systems in two or three spatial dimensions, we need to take into account also the effect of rotations. In this case, we need to introduce a physical quantity called the angular momentum, that is, themomentum induced by or connected with rotations. In classical physics the angular momentum of a particle about a given origin is defined by [see Fig. 8.1]