Aharonov-Bohm effect and superoscillations

Abstract

The path-integral technique in quantum mechanics provides an intuitive framework for comprehending particle propagation and scattering. Calculating the propagator for the Aharonov-Bohm potential fits into the range of potentials in multiply-connected spaces, with the propagator represented through a series expansion. In this paper, we analyze the Schrödinger evolution of superoscillations, showing the supershift properties of the solution to the Schrödinger equation for this potential. Our proof is based on the continuity of particular infinite order differential operators acting on spaces of entire functions.