Aharonov-Bohm effect is one of the most fascinating discoveries of the 20th century.

Here is a typical problem where Aharonov-Bohm effect appear:

An electron is inside of a sphere with radius 5 Å. Mass and thickness of the sphere are negligible. However, electromagnetic fields freely pass through the sphere without reflection or attenuation. The shell is confined to a circular track of radius 50 Å. A solenoid of radius 1 Å is perpendicular to the track, passing through its center. A magnetic filed inside of the solenoid is B and 0 outside. Describe the eigenstates of the system.

At first glance it seems simple. But how would you solve it?

The solution will be provided in the next post - stay tuned!