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Relating systems properties of the wave and the Schrödinger equation

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


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