Reconstructing the potential for the one-dimensional Schrödinger equation from boundary measurements

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Reconstructing the potential for the one-dimensional Schrödinger equation from boundary measurements. / Avdonin, S.A.; Mikhaylov, V.S.; Ramdani, K.

In: IMA Journal of Mathematical Control and Information, Vol. 31, No. 1, 2014, p. 137-150.

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

Author

Avdonin, S.A. ; Mikhaylov, V.S. ; Ramdani, K. / Reconstructing the potential for the one-dimensional Schrödinger equation from boundary measurements. In: IMA Journal of Mathematical Control and Information. 2014 ; Vol. 31, No. 1. pp. 137-150.

BibTeX

@article{2434aa4adc214ebfa949ee9c4cee7c3d,

title = "Reconstructing the potential for the one-dimensional Schr{\"o}dinger equation from boundary measurements",

abstract = "We consider the inverse problem of determining the potential in the dynamical Schr{\"o}dinger equation on the interval by the measurement on the boundary. We use the boundary control method to recover the spectrum of the problem from the observation at either left or right endpoints. Using the specificity of the one-dimensional situation, we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only a finite number of eigenvalues are known and prove the convergence of the method. {\textcopyright} 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.",

author = "S.A. Avdonin and V.S. Mikhaylov and K. Ramdani",

year = "2014",

doi = "10.1093/imamci/dnt009",

language = "English",

volume = "31",

pages = "137--150",

journal = "IMA Journal of Mathematical Control and Information",

issn = "0265-0754",

publisher = "Oxford University Press",

number = "1",

}

RIS

TY - JOUR

T1 - Reconstructing the potential for the one-dimensional Schrödinger equation from boundary measurements

AU - Avdonin, S.A.

AU - Mikhaylov, V.S.

AU - Ramdani, K.

PY - 2014

Y1 - 2014

N2 - We consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. We use the boundary control method to recover the spectrum of the problem from the observation at either left or right endpoints. Using the specificity of the one-dimensional situation, we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only a finite number of eigenvalues are known and prove the convergence of the method. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

AB - We consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. We use the boundary control method to recover the spectrum of the problem from the observation at either left or right endpoints. Using the specificity of the one-dimensional situation, we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only a finite number of eigenvalues are known and prove the convergence of the method. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

U2 - 10.1093/imamci/dnt009

DO - 10.1093/imamci/dnt009

M3 - Article

VL - 31

SP - 137

EP - 150

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

SN - 0265-0754

IS - 1

ER -

ID: 7010087