Relating systems properties of the wave and the Schrödinger equation

Heiko J. Zwart; Yann Le Gorrec; B.M. Maschke

doi:10.3934/eect.2015.4.233

Relating systems properties of the wave and the Schrödinger equation

Heiko J. Zwart, Yann Le Gorrec, B.M. Maschke

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

1 Citation (Scopus)

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	Undefined
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

MSC-93B07
MSC-93C20
MSC-35Q41
EWI-26604
IR-99221
Schrödinger equation
Well-posedness
Wave equation
METIS-315606
Exact observability

Access to Document

10.3934/eect.2015.4.233

http://eprints.eemcs.utwente.nl/secure2/26604/01/EECT_2015_Zwart.pdf

Cite this

@article{7044268cae4447abbb11b767a5f02d95,

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 = "MSC-93B07, MSC-93C20, MSC-35Q41, EWI-26604, IR-99221, Schr{\"o}dinger equation, Well-posedness, Wave equation, METIS-315606, Exact observability",

author = "Zwart, {Heiko J.} and {Le Gorrec}, Yann and B.M. Maschke",

note = "eemcs-eprint-26604 ; http://eprints.ewi.utwente.nl/26604 ",

year = "2015",

month = jun,

doi = "10.3934/eect.2015.4.233",

language = "Undefined",

volume = "4",

pages = "233--240",

journal = "Evolution equations and control theory",

issn = "2163-2472",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Relating systems properties of the wave and the Schrödinger equation

AU - Zwart, Heiko J.

AU - Le Gorrec, Yann

AU - Maschke, B.M.

N1 - eemcs-eprint-26604 ; http://eprints.ewi.utwente.nl/26604

PY - 2015/6

Y1 - 2015/6

N2 - 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.

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 - MSC-93B07

KW - MSC-93C20

KW - MSC-35Q41

KW - EWI-26604

KW - IR-99221

KW - Schrödinger equation

KW - Well-posedness

KW - Wave equation

KW - METIS-315606

KW - Exact observability

U2 - 10.3934/eect.2015.4.233

DO - 10.3934/eect.2015.4.233

M3 - Article

VL - 4

SP - 233

EP - 240

JO - Evolution equations and control theory

JF - Evolution equations and control theory

SN - 2163-2472

IS - 2

ER -