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.

arXiv comment24 pages, 9 figures, textual improvements

References in corpus (3)

• Inside-Outside Duality for Planar Billiards -- A Numerical Study
• The boundary integral method for magnetic billiards
• Relevance of Chaos in Numerical Solutions of Quantum Billiards

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