Stern-Gerlach Experiment with Higher Spins

TL;DR

This paper analyzes idealized sequential Stern-Gerlach experiments with higher spins to clarify misconceptions, improve understanding of Wigner rotations, and provide explicit probability formulas for spins 1/2, 1, and 2.

Contribution

It extends the analysis of Stern-Gerlach experiments to higher spins, offering clearer insights and explicit formulas, addressing misconceptions from the spin-1/2 case.

Findings

Explicit probability formulas for spins 1/2, 1, and 2

Clarification of misconceptions in spin-1/2 experiments

Enhanced understanding of Wigner rotation matrices

Abstract

We analyze idealized sequential Stern-Gerlach experiments with higher spin particles. This analysis serves at least two purposes: The widely discussed spin-1/2 case leads to some misunderstandings which hopefully is removed by the higher spin discussion. Secondly, Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatuses for generic spins. We work out the spin-$1/2$, spin-$1$ and spin-$2$ cases explicitly. Since there are some confusing issues regarding the actual experiment, we also compile a "facts and fiction" section on the SG experiments.