Chapter 29. Angular Momentum

Dennis Morris

A. R. Edmonds

Steven M. Pascal

The motion in the angular dimensions described by the solutions in Chapter 14 are related to angular momentum. We explore that relationship in this chapter. This gives insight into the angular TISE, showing that the equation amounts to the classical equation relating angular momentum, moment of inertia, and rotational kinetic energy: KE = L 2 /2I. This also shows that angular momentum is both conserved and quantized in a radial potential. These quantized angular momenta levels are well known to students of chemistry as the orbitals, for which the orbital angular momentum quantum number equals 0, 1, 2, and 3 for the s, p, d, and f orbital, respectively. This quantum number represents the amount of orbital angular momentum of the electron, but the calculation is a little bit more complicated, and is related to the separation constants introduced in Chapter 14 .

Will Raven

Abstract In this chapter, we explore angular momentum, a key concept in quantum mechanics and atomic physics. We cover the quantization of angular momentum, the role of quantum numbers, and their impact on atomic states. We will learn about the different types of angular momentum, the states representing these types of angular momentum, and how angular momenta are added together in quantum mechanics. The chapter also examines the compatibility of different observables, such as the magnitude and components of angular momentum, and the impact of measurements on quantum states.