Classical and Quantum Spin Angular Momentum

P. C. W. Davies, David S. Betts

One of the most important applications of the quantum mechanical formalism developed in the previous chapter is to angular momentum. This is because many microsystems are spherically symmetric, or approximately so, and angular momentum is therefore conserved. This chapter discusses that a careful study of quantized angular momentum leads to a completely new physical phenomenon – intrinsic spin. The fact that the angular momentum vector of a quantum particle must point in certain restricted directions is a bizarre quantum property. In some respects the abstract idea of an internal angular momentum is reminiscent of the classical concept of a spinning body. In classical mechanics angular momentum is added vectorially but in the quantum case the issue is more subtle. The procedure will be illustrated by the example of the addition of two spins. As in classical mechanics a charged quantum system with angular momentum possesses a magnetic moment μ.

K. Heyde, John L. Wood

A Norcliffe

The classical and quantal theories of angular momentum and spin are related using the spherical top as a model. The quantum mechanical spectral operator kernel of the spherical top is evaluated and expressed exactly as a sum over classical paths of terms containing the classical action. A relation between corresponding values of the classical and quantal angular momentum is obtained which holds for all values of the angular momentum quantum number.

Paul L. Corio

Nandita Rudra

The angular momentum operator is closely related to rotation in space. The quantum mechanical definition of angular momentum differs from the classical definition r × p of angular momentum. This expression is not sufficiently general as it cannot yield spin angular momentum which does not have a classical counterpart without having any coordinate representation.