Consolidating boundary methods for finding the eigenstates of billiards

Doron Cohen; Natasha Lepore; Eric J. Heller

doi:10.1088/0305-4470/37/6/013

Consolidating boundary methods for finding the eigenstates of billiards

Doron Cohen, Natasha Lepore, Eric J. Heller

Department of Physics

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

15 Scopus citations

Abstract

The plane-wave decomposition method, a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the gauge freedom method is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.

Original language	English
Pages (from-to)	2139-2161
Number of pages	23
Journal	Journal of Physics A: Mathematical and General
Volume	37
Issue number	6
DOIs	https://doi.org/10.1088/0305-4470/37/6/013
State	Published - 13 Feb 2004

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

Access to Document

10.1088/0305-4470/37/6/013

Cite this

@article{4bc2717d5a144cdba994100342a57f41,

title = "Consolidating boundary methods for finding the eigenstates of billiards",

abstract = "The plane-wave decomposition method, a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the gauge freedom method is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.",

author = "Doron Cohen and Natasha Lepore and Heller, {Eric J.}",

year = "2004",

month = feb,

day = "13",

doi = "10.1088/0305-4470/37/6/013",

language = "English",

volume = "37",

pages = "2139--2161",

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

issn = "0305-4470",

publisher = "IOP Publishing Ltd.",

number = "6",

}

TY - JOUR

T1 - Consolidating boundary methods for finding the eigenstates of billiards

AU - Cohen, Doron

AU - Lepore, Natasha

AU - Heller, Eric J.

PY - 2004/2/13

Y1 - 2004/2/13

N2 - The plane-wave decomposition method, a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the gauge freedom method is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.

AB - The plane-wave decomposition method, a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the gauge freedom method is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.

UR - http://www.scopus.com/inward/record.url?scp=1342283703&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/6/013

DO - 10.1088/0305-4470/37/6/013

M3 - Article

AN - SCOPUS:1342283703

SN - 0305-4470

VL - 37

SP - 2139

EP - 2161

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 6

ER -

Consolidating boundary methods for finding the eigenstates of billiards

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this