Visualizing spin states using the spin coherent state representation

Abstract

Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonics. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical analog. Many textbooks give a heuristic and somewhat unsatisfying picture of a precessing spin vector. Here, we show that the spin-coherent-state representation is a striking, elegant, and mathematically meaningful tool for visualizing spin states. We also demonstrate that cartographic projections such as the Hammer projection are useful for visualizing functions defined on spherical surfaces.