Consolidating boundary methods for finding the eigenstates of billiards

Doron Cohen, Natasha Lepore, Eric J. Heller

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)2139-2161
Number of pages23
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number6
DOIs
StatePublished - 13 Feb 2004

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