Central Forces and Angular Momentum

Pedro Pereyra Padilla

James K. Freericks

In this chapter, we develop the background needed to move our quantum mechanical formalism fully into three dimensions. We discuss angular momentum, which is the motional complement to spin angular momentum, that we developed earlier. There are some critical differences between orbital and spin angular momentum, and we need to carefully discuss how they relate and how they differ. Why is angular momentum so important? Because in problems where we have central forces (forces that depend only on the distance between two particles and act along the line connecting the two particles), the angular momentum is conserved. So, it becomes an integral part of how we solve the problem. The most important problem we have to solve, the hydrogen atom, is a central force problem; hence, we need this work before we can move forward to some really interesting physics that will come in Chap. 11 . We cover the angular momentum operators, eigenvalues, and eigenstates, their matrix representations, how to combine angular momentum, and spherical harmonics. We revisit the EPR experiment using our new formalism. We also discuss some unique representations of angular momentum by mapping to two-dimensional harmonic oscillators, as developed by Schwinger.

Bipin R. Desai

Keith Hannabuss

Abstract In many of the systems studied in classical mechanics angular momentum is far more useful than ordinary linear momentum. For example, in the study of planetary orbits, or indeed any motion under a central force, the conservation of angular momentum plays a crucial role. We shall therefore turn our attention to the description of angular momentum in quantum mechanics.

‎Louis Marchildon

Dai Meng-kun

We discuss the motion of a particle which spin is 1/2 in a central force field in two different methods. We can get the wave function of a particle by matrix operating and vector coupling theory of the angular momentum. The results is the same, so that the coupling theory of the angular momentum is correct.