Angular Momentum in Quantum Mechanics

Abstract

Before starting a detailed discussion on the underlying mechanisms that establish the nuclear shell model, not only for the single-particle degrees of freedom and excitations but also in order to study nuclei where a number of valence nucleons (protons and/or neutrons) are present outside closed shells, the quantum mechanical methods are discussed in some detail. We discuss both angular momentum in the framework of quantum mechanics and the aspect of rotations in quantum mechanics with some side-steps to elements of groups of transformations. Although in these Chaps. 1 and 2, not everything is proved, it should supply all necessary tools to tackle the nuclear shell model with success and with enough background to feel at ease when manipulating the necessary “Racah”-algebra (Racah 1942a, 1942b, 1943, 1949, 1951) needed to gain better insight in how the nuclear shell model actually works. These two chapters are relatively self-contained so that one can work through them without constant referral to the extensive literature on angular momentum algebra. More detailed discussions are in the appendices. We also include a short summary of often used expressions for the later chapters.