# Aharonov–Bohm effect - electric effect

## Description

The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential (V, A), despite being confined to a region in which both the magnetic field B and electric field E are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle’s wave function, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.

The magnetic Aharonov–Bohm effect can be seen as a result of the requirement that quantum physics be invariant with respect to the gauge choice for the electromagnetic potential, of which the magnetic vector potential A forms part.

From the Schrödinger equation, the phase of an eigenfunction with energy E goes as exp(-iEt/h). The energy, however, will depend upon the electrostatic potential V for a particle with charge q. In particular, for a region with constant potential V (zero field), the electric potential energy qV is simply added to E, resulting in a phase shift calculated by the shown formula

Related formulas## Variables

Δϕ | phase shift (dimensionless) |

q | particle charge (C) |

V | particle electrostatic potential (volt) |

t | time spent in the potential (s) |

h | Planck constant |