Consolidating boundary methods for finding the eigenstates of billiards

Abstract

The plane-wave decomposition method (PWDM), 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 (GFM) is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.

24 pages, 9 figures, textual improvements

References in corpus (2)

• The boundary integral method for magnetic billiards
• Relevance of Chaos in Numerical Solutions of Quantum Billiards

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