Eigenstates for billiards of arbitrary shapes

Details Eigenstates for billiards of arbitrary shapes Eigenstates for billiards of arbitrary shapes

1999-02-20

arxiv.org/abs/physics/9902057v1

Physics

Computational Physics

14 pages, 3 figures, submitted to Phys. Rev. E

Scientific paper

A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from the limitations associated with the shape of the billiard and could be applied even for nonconvex geometries where other algorithms face difficulties. Moreover it does not suffer from the existence of eigenvalue degeneracies which is another serious shortcoming of many methods. In the paper we apply the algorithm to a few simple cases where the analytical solutions exist. Numerical solutions have been investigated for the case of annular billiard.

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