Relating systems properties of the wave and the Schrödinger equation

Hans Zwart; Yann Le Gorrec; Bernhard Maschke

doi:10.3934/eect.2015.4.233

Relating systems properties of the wave and the Schrödinger equation

Hans Zwart, Yann Le Gorrec, Bernhard Maschke

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Abstract

In this article we show that systems properties of the systems governed by the second order differential equation d2wdt2=−A0w and the first order differential equation dzdt=iA0z 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.

Original language	English
Pages (from-to)	233-240
Number of pages	8
Journal	Evolution equations and control theory
Volume	4
Issue number	2
DOIs	https://doi.org/10.3934/eect.2015.4.233
Publication status	Published - Jun 2015

Keywords

Exact observability
Schrodinger equation
Wave equation
Well-posedness
2023 OA procedure

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10.3934/eect.2015.4.233

ArticleFinal published version, 314 KBLicence: Taverne

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title = "Relating systems properties of the wave and the Schr{\"o}dinger equation",

abstract = "In this article we show that systems properties of the systems governed by the second order differential equation d2wdt2=−A0w and the first order differential equation dzdt=iA0z 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 Schr{\"o}dinger equation.",

keywords = "Exact observability, Schrodinger equation, Wave equation, Well-posedness, 2023 OA procedure",

author = "Hans Zwart and {Le Gorrec}, Yann and Bernhard Maschke",

year = "2015",

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AU - Le Gorrec, Yann

AU - Maschke, Bernhard

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AB - In this article we show that systems properties of the systems governed by the second order differential equation d2wdt2=−A0w and the first order differential equation dzdt=iA0z 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.

KW - Exact observability

KW - Schrodinger equation

KW - Wave equation

KW - Well-posedness

KW - 2023 OA procedure

U2 - 10.3934/eect.2015.4.233

DO - 10.3934/eect.2015.4.233

M3 - Article

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VL - 4

SP - 233

EP - 240

JO - Evolution equations and control theory

JF - Evolution equations and control theory

IS - 2

ER -

Relating systems properties of the wave and the Schrödinger equation

Abstract

Keywords

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