PERSISTENCE OF SUPEROSCILLATIONS UNDER THE SCHRÖDINGER EQUATION

The goal of this paper is to provide new proofs of the persistence of superoscillations under the Schrödinger equation. Superoscillations were first put forward by Aharonov and have since received much study because of connections to physics, engineering, signal processing and information theory. An interesting mathematical question is to understand the time evolution of superoscillations under certain Schrödinger equations arising in physics. This paper provides an alternative proof of the persistence of superoscillations by some elementary convergence facts for sequence and series and some connections with certain polynomials and identities in combinatorics. The approach given opens new perspectives to establish persistence of superoscillations for the Schrödinger equation with more general potentials.