The quantum spectra analysis of the circular billiards in wells |
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| Authors: | Zhang Yan-Hui Zhang Li-Qin Xu Xue-You Ge Mei-Hu Lin Sheng-Lu Du Meng-Li |
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| Affiliation: | College of Physics and Electronics, Shandong Normal University, Jinan 250014, China; Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics. |
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| Keywords: | circular billiard closed-orbit theory quantum spectra function Fourier-transformed spectra |
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