Quantum Electrodynamics & Gauge Fields

Aharonov-Bohm Effect

Simulate Yakir Aharonov and David Bohm's 1959 quantum gauge phase experiment. Electron wavepaths encircling a shielded magnetic solenoid ($B = 0$ outside) undergo quantum phase shift $\Delta\phi = \frac{e \Phi_B}{\hbar}$ from magnetic vector potential $\vec{A}$.

Magnetic Flux Φ_B 1.00 Φ₀ (hc/e)

Quantum Phase Shift Δφ π rad (180°)

Field B Outside Solenoid 0.00 T (Zero Field)

Solenoid Flux Setup

Magnetic Flux Φ_B 1.0 Φ₀

Visual Overlay

Show Vector Potential A Circles

Show Interference Fringe Pattern

Show Solenoid & Path Badges

Controls

Vector Potential & Quantum Gauge Phase Equations

Vector Potential Outside Solenoid: A(r) = (Φ_B / 2π r) · φ̂ (where B = ∇ × A = 0)
Quantum Wavefunction Phase: ψ(r) = ψ₀(r) · exp[ (i e / ℏ) ∫ A · dr ]
Aharonov-Bohm Phase Shift: Δφ = (e / ℏ) ∮ A · dr = e Φ_B / ℏ = 2π (Φ_B / Φ₀)

Developer Reference

Core Algorithm & Standalone Script

// Aharonov-Bohm quantum gauge vector potential solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// delta_phi = (e / hbar) * flux