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Physics Bulletin

Elementary Theory of Angular Momentum

Leo Pincherle

Published Feb 1, 1958• 2,786 citations
Publisher

Abstract

By M. E. Rose London : Chapman & Hall Ltd. Pp. x + 248. Price 80s. The theory of angular momentum has long been of importance in spectroscopy, and those interested in the subject twenty-five years ago had to find their way rather painfully through highly formal textbooks and papers. The theory has lately become even more important mainly because of improvements in experimental techniques for measuring angular distributions or angular correlations in nuclear physics, and because of problems in low-temperature studies and in microwave spectroscopy involving static moments coupled to fields arising from surrounding charges.

DOI
10.1088/0031-9112/9/2/013

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By M. E. Rose London : Chapman & Hall Ltd. Pp. x + 248. Price 80s. The theory of angular momentum has long been of importance in spectroscopy, and those interested in the subject twenty-five years ago had to find their way rather painfully through highly formal textbooks and papers. The theory has lately become even more important mainly because of improvements in experimental techniques for measuring angular distributions or angular correlations in nuclear physics, and because of problems in low-temperature studies and in microwave spectroscopy involving static moments coupled to fields arising from surrounding charges.
This is the most complete handbook on the quantum theory of angular momentum. Containing basic definitions and theorems as well as relations, tables of formula and numerical tables which are essential for applications to many physical problems, the book is useful for specialists in nuclear and particle physics, atomic and molecular spectroscopy, plasma physics, collision and reaction theory, quantum chemistry, etc. The authors take pains to write many formulae in different coordinate systems thus providing users with added ease in consulting this book. Each chapter opens with a comprehensive list of its contents to ease the search for any information needed later. New results relating to different aspects of the angular momentum thoery are also included. Containing close to 500 pages this book also gathers together many useful formulae besides those related to angular momentum. The book also compares different notations used by previous authors.
Chapter 11 is devoted to the quantum theory of angular momentum. As in classical mechanics, working with angular momentum requires leaving the one-dimensional space, with all the complications that this entails. The importance of angular momentum resides in at least three facts: i) central problems are of particular interest; (ii) many particles have an intrinsic angular momentum (the spin); and iii) the physics of angular momentum involves features such as the so-called space quantization. The first part of the chapter deals with the orbital angular momentum and its eigenfunctions, the spherical harmonics. Its algebraic properties, embodied in the matrix representation, allow for an extension of the theory to half-integer angular momentum in terms of Pauli matrices, as well as the addition of angular momenta.
Angular momentum is a very important and revealing property of many physical systems. In classical mechanics the principle of conservation of angular momentum is a powerful aid to the solution of such problems as the orbits of planets and satellites and the behaviour of gyroscopes and tops. The role of angular momentum in quantum mechanics is probably even more important and this will be the subject of the present chapter and the next. We shall find that the operators representing the components of angular momentum do not commute with each other, although they all commute with the operator representing the total angular momentum. It follows that no pair of these components can be measured compatibly and we shall therefore look for a set of eigenfunctions that are common to the operators representing the total angular momentum and one of its components. We shall find that the angular momentum eigenvalues always form a discrete set and that, in the case of a central field, the operators commute with the Hamiltonian, implying that the total angular momentum and one component can be measured compatibly with the energy in this case, so that their values, once measured, remain constant in time. Consideration of angular momentum will also enable us to make predictions about the behaviour of atoms in magnetic fields, and we shall find that these are in agreement with experiment only if we assume that the electron (in common with many other fundamental particles) has an intrinsic “spin” angular momentum in addition to the “orbital” angular momentum associated with its motion. The interaction between spin and orbital angular momenta leads to detailed features of the atomic spectra which are known as “fine structure.” We shall also use the measurement of angular momentum to illustrate the quantum theory of measurement discussed in the previous chapter.