半圆和四分之一圆二维弹子球的量子谱分析

The quantum spectral analysis of the semicircular and a quarter of circular billiards

采用近来提出的量子谱函数,我们把闭合轨道理论应用到半圆和四分之一圆弹子球系统,这种量子谱函数的傅利叶变换包含了连接任意两点的许多经典轨道的信息.计算表明量子谱的傅立叶变换和经典轨道的长度符合的很好.从这两个体系可以看出半经典理论为经典和量子力学提供了很好的桥梁作用.

Using a recently defined quantum spectral function and the method of closed-orbit theory we studied the spectra of the half-circular and the quarter circular billiard systems for arbitrary two points. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in well. Our calculation demonstrates that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. The two examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.