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Quantization of Sinai's Billiard - A Scattering Approach

Holger Schanz·Uzy Smilansky
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Abstract

We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method provides an efficient numerical scheme, and its implementation for the present case gives a few thousands of levels without encountering any serious difficulty. We use the numerical data to check some approximations which are essential for the derivation of a semiclassical quantization method based also on this scattering approach.

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Holger Schanz, Uzy Smilansky. 1995-02-25. Quantization of Sinai's Billiard - A Scattering Approach. https://doi.org/10.1016/0960-0779(94)e0066-x

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