Quantum Mechanics & Spin

Stern-Gerlach Experiment

Simulate Otto Stern and Walther Gerlach's 1922 experiment. Pass silver atoms through an inhomogeneous magnetic field $\partial B_z / \partial z$ to observe spatial quantization of spin $S_z = \pm \hbar / 2$ splitting into two discrete beams.

Spin-Up |↑⟩ Count 245 (50.1%)

Spin-Down |↓⟩ Count 243 (49.9%)

Field Gradient dB/dz 10.0 T/m

Magnet Setup

Field Gradient dB/dz 10 T/m

Measurement Axis

Visual Overlay

Show Oven, Magnet & Screen Badges

Show Quantum Spin Vectors |↑⟩ / |↓⟩

Show Detector Screen Hit Pattern

Controls

Quantum Spin Deflection Formula

Deflection Force: F_z = μ_z · (∂B_z / ∂z) = ± (g_s μ_B / 2) · (∂B_z / ∂z)
Spin Projection: S_z = ± ℏ / 2 (Discrete 2-level quantum system)
Classical Prediction: Continuous ellipse | Quantum Result: Exactly 2 separated spots!

Developer Reference

Core Algorithm & Standalone Script

// Stern-Gerlach quantum spin deflection simulator
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// F_z = +/- (g_s * mu_B / 2) * (dB_z / dz)