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- W2034766728 abstract "There is theoretical evidence indicating that generic polygons do not admit eigenfunctions that are superpositions of plane waves. However, we find that a plane-wave quantization for a family of polygonal billiards gives results in very good agreement with theoretical predictions. Indeed the fraction of missing states decreases as the number of sides is increased. We provide a resolution of this contradiction: While theory says that no plane-wave eigenfunctions are possible for polygonal boundaries, it is not applicable to the curvilinear boundaries approximating these polygons. This is analogous to the classical mechanics of polygonal billiards, where according to continuum mathematics there is no chaos, yet discrete mathematics finds it. In the quantum treatment considered here, according to continuum mathematics there can be no plane-wave eigenfunctions, yet discrete mathematics finds them." @default.
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- W2034766728 date "1995-08-01" @default.
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- W2034766728 title "Plane-wave quantization for polygonal billiards" @default.
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- W2034766728 doi "https://doi.org/10.1103/physreve.52.1490" @default.
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