How superoscillating tunneling waves can overcome the step potential

Y. Aharonov, F. Colombo*, I. Sabadini, D. C. Struppa, J. Tollaksen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the Cauchy problem for the Schrödinger equation with step potential with jump V0 at the origin and whose initial datum is a superoscillatory function Fn that is traveling from −∞ in the direction of the barrier V0. We assume that the energies En,k of all the traveling waves en,kx with |λn,k|≤1, are strictly less then the potential V0 (n and k are suitable natural numbers), so that all the waves en,kx are subjected to the tunnel effect for x≥0. We prove that in the limit, as n tends to infinity, from the infinitely many tunneling waves en,kx emerges a wave that passes through the potential barrier. In other words, we prove that superoscillations overcome the potential barrier of the step potential even though none of its constituent waves can.

Original languageEnglish
Article number168088
JournalAnnals of Physics
StatePublished - Mar 2020
Externally publishedYes


FundersFunder number
Chapman University


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