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Title: Quantum harmonic oscillator with superoscillating initial datum

In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
Authors:
;  [1] ; ;  [2]
  1. Schmid College of Science and Technology, Chapman University, Orange, California 92866 (United States)
  2. Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi 9, 20133 Milano (Italy)
Publication Date:
OSTI Identifier:
22403058
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; DATA; HARMONIC OSCILLATORS; HARMONIC POTENTIAL; SINGULARITY