Aharonov-Bohm Effect

Quantum interference shifted by enclosed magnetic flux — with no classical force

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The Aharonov-Bohm effect (1959): a charged quantum particle acquires a phase shift Δφ = 2πΦ/Φ₀ when encircling a solenoid, even though the magnetic field B=0 along the particle's path. Only the vector potential A matters — a profoundly non-classical result. The interference pattern shifts continuously with enclosed flux Φ; fringe pattern is periodic with period Φ₀ = h/e (flux quantum).