Transmission through a regular vs. a superoscillating barrier

Superoscillating functions are band-limited functions that oscillate in some region faster than their largest Fourier frequency. In past years, this phenomenon triggered great scientific interest as a building block which could promote research in many fields. In this article, the effect of superoscillating coupling is investigated in the context of quantum physics. Our purpose was to find out whether a quantum system responds in the same way to a time-dependent potential oscillating at some given frequency and to the same potential oscillating at the corresponding superoscillation frequency. This is done by analyzing the quantum mechanics of a one-dimensional particle in the presence of a time dependent delta function potential. The main finding obtained by numerical solution of the Schrodinger equation is that in a carefully prepared situation, the responses in those two cases are similar.