Quantum Mechanics
Aharonov-Bohm: Computer experiment

The following animation shows the diffraction of a Gaussian wave packet by two slits. In this case there is no magnetic field.

Diffraction of Gaussian wave packet by two slits, no magnetic field

The angular distribution I (theta) recorded by a detector placed far away from a source characterizes the interference pattern. For zero magnetic fieldSchematic picture of source and detector screen to measure I (theta) the simulation yields an angular distribution I (theta) that is in excellent agreement with the Fraunhofer diffraction pattern of a double slit.

The next animation illustrates the Aharonov-Bohm effect. The magnetic field is confined to the red area and is chosen such that the shift in the interference pattern is as large as possible.

Diffraction of Gaussian wave packet by two slits, magnetic field

Inspection of the angular distribution shows that compared to the zero field case the maxima and the minima are interchanged:

Angular distribution for B = 0 and B = B'

The diffraction pattern is shifted by an angle varphi. In general, varphi (B) = varphi (B+2B'), where B' is the magic field for which varphi (B) = 180^o. The interchange of maxima and minima can also be demonstrated by superimposing the animations for zero and magic magnetic field. In the animation that follows only the blue colored wave packet is affected by the vector potential.

Superposition of animations for zero and magic magnetic field