The Stern-Gerlach experiment, electron spin and intermediate quantum mechanics

Abstract

It is suggested that a thorough treatment of electron spin has advantages as a method of presenting many of the concepts and techniques of intermediate quantum mechanics. The starting point is the Stern-Gerlach experiment, from which the anticommutation relations for the spin operators may immediately be deduced. The commutation relations, which demonstrate that the spin is an angular momentum, are derived from these and it is shown that the anomalous gyromagnetic ratio is a natural consequence of the properties of the spin operators. The Pauli theory, which is the simplest example of the use of matrices in quantum mechanics, is briefly summarised, and employed in an analysis of the double Stern-Gerlach experiment. This example of a change of representation is used to introduce Dirac's transformation theory which, together with a variant of the double Stern-Gerlach experiment, is made use of in a discussion of the EPR paradox, Bell's inequality and hidden-variable theories. It is emphasised that the quantum mechanical description of these phenomena is consistent and that, from the viewpoint of quantum theory, no action-at-a-distance is required to explain them.