In quantum mechanics, a vector potential is said to have a direct significance to particles moving in a magnetic field. This quantum effect is known as the Aharonov–Bohm effect (the AB effect). We study the AB effect through resonances for scattering by three solenoids in two dimensions under the situation that the centers of the solenoids are placed almost in line. The resonances are shown to be generated near the real axis by the trapping trajectories when the centers are largely separated from one another. We analyze how the AB effect is reflected in the location of these resonances. The result is described in terms of the backward scattering amplitudes by one solenoid and depends on the ratio of the distances between the centers as well as on the magnetic fluxes. The method makes a full use of the information from scattering system by one solenoid, which is known as one of exactly solvable models in quantum mechanics. We also discuss what happens in the case of four solenoids.
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