二维量子台球体系的量子谱和经典周期轨道

Quantum Spectra and Classical Periodic Orbit in the Two-dimensional Quantum Billiard

利用周期轨道理论,对二维矩形量子台球体系的量子谱进行了计算和分析.计算结果表明:傅里叶变换量子谱中的每一条峰正好对应一条周期轨道的贡献,随着轨道长度的增加,经典周期轨道的条数增加,其所对应的量子谱中出现的峰值也相应增加,这说明经典计算的结果和量子计算的结果符合得非常好,从而进一步验证了周期轨道理论的正确性.

Using the periodic orbit theory, the quantum spectra in the two dimensional rectangular billiard are calculated and analyzed. The results show that each peak in the Fourier transformed spectrum of this system corresponds to the contribution of one classical periodic orbit ; and with the increase of the length of the orbit, the number of the classical periodic orbit increases, and the peaks in the corresponding quantum spectra have also increased. This study suggests the good correspondence between the quantum spectra and the classical orbits in the rectangular billiards. Therefore, the correctness of the periodic orbit theory has been verified, which further deepen people＇s awareness of the relations between the classical and quantum mechanics.