On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Lyonell Boulton; Michael Levitin

doi:10.1088/1751-8113/40/31/010

On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Lyonell Boulton, Michael Levitin

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

24 Citations (Scopus)

Abstract

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. © 2007 IOP Publishing Ltd.

Original language	English
Article number	010
Pages (from-to)	9319-9329
Number of pages	11
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	31
DOIs	https://doi.org/10.1088/1751-8113/40/31/010
Publication status	Published - 27 Jul 2007

Access to Document

10.1088/1751-8113/40/31/010

Cite this

@article{9af906a707a84f7a90410e9055277598,

title = "On approximation of the eigenvalues of perturbed periodic Schr{\"o}dinger operators",

abstract = "This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schr{\"o}dinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. {\textcopyright} 2007 IOP Publishing Ltd.",

author = "Lyonell Boulton and Michael Levitin",

year = "2007",

month = jul,

day = "27",

doi = "10.1088/1751-8113/40/31/010",

language = "English",

volume = "40",

pages = "9319--9329",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing ",

number = "31",

}

TY - JOUR

T1 - On approximation of the eigenvalues of perturbed periodic Schrödinger operators

AU - Boulton, Lyonell

AU - Levitin, Michael

PY - 2007/7/27

Y1 - 2007/7/27

N2 - This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. © 2007 IOP Publishing Ltd.

AB - This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. © 2007 IOP Publishing Ltd.

UR - http://www.scopus.com/inward/record.url?scp=34547424375&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/31/010

DO - 10.1088/1751-8113/40/31/010

M3 - Article

SN - 1751-8113

VL - 40

SP - 9319

EP - 9329

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 31

M1 - 010

ER -

On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Abstract

Access to Document

Other files and links

Fingerprint

Cite this