A unified approach to Schrödinger evolution of superoscillations and supershifts

Yakir Aharonov, Jussi Behrndt*, Fabrizio Colombo, Peter Schlosser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 explicit form. With this efficient general technique, we are able to treat various potentials.

Original languageEnglish
Article number26
JournalJournal of Evolution Equations
Issue number1
StatePublished - Mar 2022
Externally publishedYes


FundersFunder number
European Cooperation in Science and Technology
Austrian Science FundP 33568-N


    • Green’s function
    • Schrödinger equation
    • Superoscillating function
    • Supershift property


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