Relating systems properties of the wave and the Schrödinger equation

Hans  Zwart; Yann Le  Gorrec; Bernhard  Maschke

doi:10.3934/eect.2015.4.233

Article Contents

2015, Volume 4, Issue 2: 233-240. Doi: 10.3934/eect.2015.4.233

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Relating systems properties of the wave and the Schrödinger equation

1.
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede
2.
FEMTO-ST AS2M, Université de Franche Comté/CNRS/ENSMM/UTBM, 24 rue Alain Savary, 25000 Besançon

Received: May 2014

Revised: September 2014

Published: June 2015

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Abstract

In this article we show that systems properties of the systems governed by the second order differential equation $\frac{d^{2}w}{dt^{2}}=-A_{0}w$ and the first order differential equation $\frac{dz}{dt}=iA_{0}z$ are related. This can be used to show that, for instance, exact observability of the $N$-dimensional wave equation implies the similar property for the $N$-dimensional Schrödinger equation.

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Mathematics Subject Classification: Primary: 93C20, 93B07; Secondary: 35Q41.

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