Simulation of atom trajectories in the original Stern-Gerlach experiment

TL;DR

This paper models the Stern-Gerlach experiment's magnetic field using finite-element analysis and simulates atomic trajectories with Monte Carlo methods, accurately reproducing the experiment's quantized end-pattern.

Contribution

It provides the most precise finite-element model of the Stern-Gerlach magnetic field and simulates atom trajectories to match historical experimental results.

Findings

Accurate magnetic field modeling with finite-element method.

Simulation reproduces the quantized end-pattern.

Matches historically reported experimental values.

Abstract

Following a comprehensive analysis of the historical literature, we model the geometry of the Stern$\unicode{x2013}$Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field and Monte Carlo methods, the atomic translational dynamics are simulated to produce the well-known quantized end-pattern with matching dimensions. The finite-element method used provides the most accurate description of the Stern$\unicode{x2013}$Gerlach magnetic field and end-pattern in the literature, matching the historically reported values and figures.