Citation:
Cohen, D., Lepore, N. & Heller, E.J. Consolidating boundary methods for finding the eigenstates of billiards. Journal of Physics A: Mathematical and General 37, 2139 (2004).
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.