Relating systems properties of the wave and the Schrödinger equation

H Zwart; Y Le Gorrec; B Maschke

doi:10.3934/eect.2015.4.233

Relating systems properties of the wave and the Schrödinger equation

H Zwart, Y Le Gorrec, B Maschke

Research output: Contribution to journal › Article › Academic › peer-review

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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

Access to Document

10.3934/eect.2015.4.233

EECT_2015_ZwartFinal published version, 314 KBLicence: Taverne

Cite this

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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 = "H Zwart and {Le Gorrec}, Y and B Maschke",

year = "2015",

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publisher = "American Institute of Mathematical Sciences",

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AU - Le Gorrec, Y

AU - Maschke, B

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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

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DO - 10.3934/eect.2015.4.233

M3 - Article

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VL - 4

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EP - 240

JO - Evolution equations and control theory

JF - Evolution equations and control theory

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