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Oxford University Press eBooks

7. Spin

Stephan Blundell

Published Jun 1, 2012• 0 citations
Publisher

Abstract

‘Spin’ considers the movement of electrons orbiting around the nucleus of an atom. Physicists such as Wolfgang Pauli, Pieter Zeeman, Ralph Kronig, George Uhlenbeck, Samuel Goudsmit, Llewellyn Thomas, Otto Stern, and Walther Gerlach spent many years trying to solve the puzzle of electron spin through different experiments. The mathematical theory of spin began to be developed in the 1920s, but it was the work of Paul Dirac in 1928 that solved the problem. By fusing relativity and quantum mechanics, the two great products of the early 20th-century revolution in physics, Dirac had assembled an equation that describes the origin of spin, the fundamental element of the magnetism of the electron.

DOI
10.1093/actrade/9780199601202.003.0007

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In the introductory remarks to Chapter 5 mention was made of the 1925 proposal of Uhlenbeck and Goudsmit that to an electron there should be assigned an intrinsic angular momentum or spin S = (S x , S y , S z )—this in addition to its quantum angular momentum (or orbital angular momentum) M = (M x , M y , M z ) defined in (5.4.4). This is not to be taken to mean that an electron actually spins about an axis in some physical way. Experiments (in particular the noted Stern-Gerlach experiment) have provided adequate justification for the proposed concept of spin, a proposal also made by R. Bichowsky and H. Urey. Dirac has shown that the notion of spin is necessary if quantum mechanics and Einstein relativity are to be consistent theories. Chemical properties of atoms, and their ability to combine and form molecules, the splitting of spectral lines by a magnetic field applied to an atom (i.e., the Zeeman effect, which we discuss later), all depend on this important notion.

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Abstract We have seen in the preceding episode that early in 1925 Pauli attributed to the electron a ‘classically not describable two-valuedness’. Within a few months this property of the electron was given a physical description which, it is true, is not satisfactory from the viewpoint of classical physics. This description is regarded as the discovery of the intrinsic angular momentum or spin of the electron. In fact the description was given twice. Already in January Kronig discussed it with Pauli who was completely opposed to the idea so that Kronig did not publish it. The concept of the electron spin was independently proposed and published [1] by Uhlenbeck and Goudsmit who thus became the discoverers of spin.

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Spin

Goudsmit, Samuel A. It was a little over fifty years ago that George Uhlenbeck and I introduced the concept of spin. . . It is therefore not surprising that most young physicists do not know that spin had to be introduced. They think that it was revealed in Genesis or perhaps postulated by Sir Isaac Newton, which most young physicists consider to be about simultaneous.

CRC Press eBooks•Aug 1, 2003•0 citations
‘Spin’ considers the movement of electrons orbiting around the nucleus of an atom. Physicists such as Wolfgang Pauli, Pieter Zeeman, Ralph Kronig, George Uhlenbeck, Samuel Goudsmit, Llewellyn Thomas, Otto Stern, and Walther Gerlach spent many years trying to solve the puzzle of electron spin through different experiments. The mathematical theory of spin began to be developed in the 1920s, but it was the work of Paul Dirac in 1928 that solved the problem. By fusing relativity and quantum mechanics, the two great products of the early 20th-century revolution in physics, Dirac had assembled an equation that describes the origin of spin, the fundamental element of the magnetism of the electron.
In the introductory remarks to Chapter 5 mention was made of the 1925 proposal of Uhlenbeck and Goudsmit that to an electron there should be assigned an intrinsic angular momentum or spin S = (S x , S y , S z )—this in addition to its quantum angular momentum (or orbital angular momentum) M = (M x , M y , M z ) defined in (5.4.4). This is not to be taken to mean that an electron actually spins about an axis in some physical way. Experiments (in particular the noted Stern-Gerlach experiment) have provided adequate justification for the proposed concept of spin, a proposal also made by R. Bichowsky and H. Urey. Dirac has shown that the notion of spin is necessary if quantum mechanics and Einstein relativity are to be consistent theories. Chemical properties of atoms, and their ability to combine and form molecules, the splitting of spectral lines by a magnetic field applied to an atom (i.e., the Zeeman effect, which we discuss later), all depend on this important notion.
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 .
This article is dedicated to the 100th anniversary of quantum mechanics, and in particular to electron spin Ð a phenomenon that has no counterpart in classical physics.The hypothesis of electron spin was proposed by Uhlenbeck and Goudsmit in 1925±1926 to explain numerous experimental data.Two years later, Dirac discovered the existence of electron spin when constructing the relativistic wave equation for a free particle.This came as a great surprise to Dirac, since, as he later claimed (in 1977), his goal was to obtain a relativistic wave equation for the simplest particle, which he considered to be a particle with zero spin.But it turned out that the simplest particle is one with spin 1a2.
Abstract This chapter gets into the heart of the discovery of spin in physics as physicists try to make sense of the atomic spectra with the discovery of the anomalous Zeeman effect by Thomas Preston before the dawn of the twentieth century as Nature gave the first signal of the existence of quantum spin. Following Bohr, Sommerfeld, and Lande’s contributions with integers and then half-integers, quantum numbers make appearances, and after Uhlenbeck and Goudsmit’s ground-breaking contributions, physicists finally embrace the idea that electron spins. Pauli’s introduction of quantum spin with Pauli matrices provided a non-relativistic theory of the quantum spin. Hestenes argues that spin is not intrinsically related to Pauli matrices, and contrary to conventional wisdom, he advocates the view that the spin is very much present in the non-relativistic quantum physics.
Abstract We have seen in the preceding episode that early in 1925 Pauli attributed to the electron a ‘classically not describable two-valuedness’. Within a few months this property of the electron was given a physical description which, it is true, is not satisfactory from the viewpoint of classical physics. This description is regarded as the discovery of the intrinsic angular momentum or spin of the electron. In fact the description was given twice. Already in January Kronig discussed it with Pauli who was completely opposed to the idea so that Kronig did not publish it. The concept of the electron spin was independently proposed and published [1] by Uhlenbeck and Goudsmit who thus became the discoverers of spin.