Scattering by magnetic fields and Aharonov-Bohm effect

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The present project has been devoted to the study on the scattering problem by several point-like magnetic fields in two dimensions. According to the Aharonov-Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point-like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained result depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values obtained from the asymptotic formula for the differential cross sections and we see how the pattern of interferences changes with flux parameters.