Angular Momentum Theory

James D. Louck

Ana Marı́a Cetto, Luis de la Peña

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.

Gennaro Auletta, Shang-Yung Wang

In this chapter we shall treat two of the most important observables of quantum mechanical systems: angular momentum and spin. We shall argue that angular momentum is the generator of rotations. In quantummechanics, angular momentum is quantized in units of the reduced Planck constant. The quantization of angular momentum is dealt with by finding the angular momentum eigenvalues and eigenstates. We shall then apply the theory of angular momentum to study the hydrogen atom. Spin is an intrinsic angular momentum of subatomic particles and therefore corresponds to an important intrinsic degree of freedom. We shall discuss briefly how spin was discovered and many of its important properties. Finally, we shall also explore here some further subtleties of quantum theory.a When we consider quantum systems in two or three spatial dimensions, we need to take into account also the effect of rotations. In this case, we need to introduce a physical quantity called the angular momentum, that is, themomentum induced by or connected with rotations. In classical physics the angular momentum of a particle about a given origin is defined by [see Fig. 8.1]

K. T. Hecht

Jochen Pade

Victor M. Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes issues that deal with the general properties of angular momentum; angular momentum, l = 1; the addition of angular momenta; and tensor formalism in angular momentum theory.