Quantum harmonic oscillator with superoscillating initial datum

Journal Article · Sat Nov 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4901753· OSTI ID:22403058

Buniy, R. V.; Struppa, D. C. ^[1]; Colombo, F.; Sabadini, I. ^[2]

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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)

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.

• OSTI ID: 22403058
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DATA
HARMONIC OSCILLATORS
HARMONIC POTENTIAL
SINGULARITY