An analysis of the diffraction of electrons by a thin wire of varied length with and without Aharonov-Bohm phase effects

Abstract

It is common during undergraduate courses to study the phenomenon of diffraction of electromagnetic waves by single and double slit systems via scalar diffraction theory and the Kirchoff integral. Alternatively, we analyze here the diffraction patterns of electrons by a barrier or thin wire of varied length, with and without Aharonov-Bohm phase effect, via Feynman path integrals. In this context we observe the gradual emergence and predominance of the different domains of optics, the physical and the geometric, in the region immediately before the obstacle, leading to a behavior complementary to that observed in simple slit diffraction, in particular, when the obstacle becomes much larger than the wavelength $\lambda$

Keywords:
Aharonov-Bohm effect; path integrals; Fresnel functions; Difraction