Intrinsic Angular Momentum and Magnetic Moment of the Electron. Spin

Ronald A. Lovett

Giampiero V. M. Esposito, Giuseppe Marmo, Gennaro Miele +1 more

First, the experimental foundations for the existence of a new dynamical variable, the spin of particles, are presented. The Pauli equation is then derived in detail, two applications are given and the energy levels of a particle with spin in a constant magnetic field are studied. This is the analysis of Landau levels, which can be performed by using the known results on the spectrum of harmonic oscillators. In this chapter we also study in detail the addition of orbital angular momentum and spin, as well as the spin–orbit interaction with the resulting Thomas precession. Stern-Gerlach experiment and electron spin The hypothesis that the electron has an intrinsic magnetic moment and an angular momentum, in short a spin , was first suggested in Uhlenbeck and Goudsmit (1926). They noticed, even before the discovery of quantum mechanics, that a complete description of spectra was not possible unless a magnetic moment and a mechanical moment were ascribed to the electron, and hence the concept of an electron as a point charge was insufficient. First, let us therefore try to understand how a magnetic moment can be associated to an atomic system. For this purpose, consider for simplicity the Bohr model of an hydrogen atom, where the electron moves along a circular orbit and rotates with orbital angular momentum L .

Robert A. Close

David C. Jiles

This chapter discusses the prime cause of the magnetic moment within an individual atom. In the classical model, the angular momentum of the electrons can be used to determine the magnetic moments of the electrons by invoking the concept of electrical charge in motion. There are two contributions to the electronic magnetic moment: an orbital magnetic moment due to orbital angular momentum and a spin magnetic moment due to electron spin. The component of orbital angular momentum along the axis of a magnetic field is restricted to discrete values by quantum mechanics. Electrons have spin angular momentum, which can be represented by the spin quantum number. As the magnetic field is increased and the field splitting becomes greater than the multiple splitting, the anomalous Zeeman effect changes over to a normal Zeeman effect. The chapter looks at experimental evidence confirming the quantization of magnetic moments, specifically the Zeeman effect and the Stern-Gerlach experiment.

O Chavoya-Aceves

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 $(n+1/2)\hbar$ 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