Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential. (15th May 2019)

• Record Type: Journal Article
• Authors: Colombo, F.; Gantner, J.; Struppa, D. C.
• Is Part Of: Proceedings. Volume 475:Number 2225(2019)
• Publication Date: 2019-05-15
• Subjects: superoscillating functions -- convolution operators -- Schrödinger equation -- entirefunctions with growth conditions; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0390
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : In recent years, we have investigated the evolution of superoscillations under Schrödinger equation with non-singular potentials. In all those cases, we have shown that superoscillations persist in time. In this paper, we investigate the centrifugal potential, which is a singular potential, and we show that the techniques developed to study the evolution of superoscillations in the case of the Schrödinger equation with a quadratic Hamiltonian apply to this setting. We also specify, in the case of the centrifugal potential, the notion of super-shift of the limit solution, a fact explained in the last section of this paper. It then becomes apparent that superoscillations are just a particular case of super-shift.