On the Cauchy problem for the Schrödinger equation with superoscillatory initial data

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

Research output: Contribution to journalArticlepeer-review

Abstract

Superoscillatory functions were introduced in Aharonov and Vaidman (1990) [5], and recently studied in detail in Aharonov et al. (2011) [2], Berry (1994) [7] and Berry and Popescu (2006) [9]. In this paper we study the time evolution of a superoscillating function, by taking it as initial value for the Cauchy problem for the Schrödinger equation. By using convolution operators on spaces of entire functions with suitable growth conditions, we prove the surprising fact that the superoscillatory phenomenon persists for all values of t.

Original languageEnglish
Pages (from-to)165-173
Number of pages9
JournalJournal des Mathematiques Pures et Appliquees
Volume99
Issue number2
DOIs
StatePublished - Feb 2013
Externally publishedYes

Keywords

  • Cauchy problem
  • Entire functions with growth conditions
  • Schrödinger equation
  • Superoscillatory functions

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