Consolidating boundary methods for finding the eigenstates of billiards

Details Consolidating boundary methods for finding the eigenstates of billiards Consolidating boundary methods for finding the eigenstates of billiards

2001-08-09

arxiv.org/abs/nlin/0108014v3

J. Phys. A 37, 2139-2161 (2004).

Nonlinear Sciences

Chaotic Dynamics

24 pages, 9 figures, textual improvements

Scientific paper

10.1088/0305-4470/37/6/013

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.

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