Quantum Physics Commons^™

A Unified Spproach To Schrödinger Evolution Of Superoscillations And Supershifts, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser

Mathematics, Physics, and Computer Science Faculty Articles and Research

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its …