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Spectra analysis of the two-dimensional elliptic billiards

Xu Xue-You Zhang Yan-Hui Huang Fa-Zhong Lin Sheng-Lu Du Meng-Li

Spectra analysis of the two-dimensional elliptic billiards

Xu Xue-You, Zhang Yan-Hui, Huang Fa-Zhong, Lin Sheng-Lu, Du Meng-Li
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Publishing process
  • Received Date:  27 January 2005
  • Accepted Date:  07 March 2005
  • Published Online:  05 May 2005

Spectra analysis of the two-dimensional elliptic billiards

  • 1. (1)山东师范大学物理与电子科学学院,济南 250014; (2)中国科学院理论物理研究所,北京 100080

Abstract: The correspondence between the quantum spectra and the classical orbits of the two-dimensional elliptic billiards is investigated. In order to study systems without analytic solutions in the future, an expansion method for stationary states (EMSS) to get highly accurate numerical solutions is applied and tested. The closed-orbit theory was extended to the open orbit case. By comparing the Fourier-transformed spectra with the classical orbits, we find that the peak positions in the quantum spectra match with the lengths of the classical orbits with small numerical differences. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.

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