vecator atom model

Introduction

Illustration of the vector model of orbital angular momentum.

The model is a convenient representation of the angular momenta of the electrons in the atom. Angular momentum is always split into orbital L, spin S and total J:

Given that in quantum mechanics, angular momentum is quantized and there is an uncertainty relation for the components of each vector, the representation turns out to be quite simple (although the background mathematics is quite complex). Geometrically it is a discrete set of right-circular cones, without the circular base, in which the axes of all the cones are lined up onto a common axis, conventionally the z-axis for three-dimensional Cartesian coordinates.^[2] Following is the background to this construction.