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The structure of additional electromagnetic fields to the Aharonov-Bohmfield, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can besolved exactly are described and the corresponding exact solutions are found.It is demonstrated that aside from the known cases (a constant and uniformmagnetic field that is parallel to the Aharonov-Bohm solenoid, a staticspherically symmetrical electric field, and the field of a magnetic monopole),there are broad classes of additional fields. Among these new additional fieldswe have physically interesting electric fields acting during a finite time, orlocalized in a restricted region of space. There are additional time-dependentuniform and isotropic electric fields that allow exact solutions of theSchrodinger equation. In the relativistic case there are additional electricfields propagating along the Aharonov-Bohm solenoid with arbitrary electricpulse shape.

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields