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

作　　者：张丽琴[1] 张延惠[1] 徐学友[1] 王雅静[1] 林圣路[1] 杜孟利[2] 

机构地区：[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

出　　处：《原子与分子物理学报》2007年第1期69-73,共5页Journal of Atomic and Molecular Physics

基　　金：国家自然科学基金(10374061;90403028)

摘　　要：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.

关 键 词：量子台球 闭合轨道理论 量子谱函数 量子与经典的对应 Fourier变换谱 

分 类 号：O365[理学—流体力学]