Stefan Giller, Jarosław Janiak
Semiclassical wave functions in billiards based on the Maslov-Fedoriuk approach are constructed. They are defined on classical constructions called skeletons which are the billiards generalization of the Arnold tori. The skeleton formulation is applied to calculate semiclassical wave functions and the corresponding energy spectra for the integrable and pseudointegrable billiards as well as in the limiting forms in some cases of chaotic ones. The superscars of Bogomolny and Schmit are shown to be simply singular semiclassical solutions of the eigenvalue problem in the billiards well built on skeletons in the billiards with flat boundaries both in the integrable, pseudointegrable and chaotic cases of such billiards
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http://arxiv.org/abs/1301.5212
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