二维心形量子台球中的谱分析  

SPECTRA ANALYSIS OF THE TWO-DIMENSIONAL OBCORDATE BILLIARDS

作　　者：周淑菊[1] 郭文豪[1] 林圣路[1] 

机构地区：[1]山东师范大学物理与电子科学学院,济南250014

出　　处：《山东师范大学学报（自然科学版）》2007年第1期39-41,共3页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10374061)

摘　　要：研究了二维心形台球的经典与量子的对应关系,运用闭合轨道理论及定态展开方法数值计算了傅立叶变换的量子谱.把傅立叶变换后的量子谱中峰的位置与其所对应的经典体系的轨道长度作对照,我们发现傅立叶变换的量子谱的峰位和经典轨道的长度之间存在很好的对应关系.于是得到混沌系统的量子经典对应,也进一步证明了闭合轨道理论的正确性.The correspondence between the quantum spectra and the classical orbits of the two-dimensional obcordate 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 with the lenths of the classical orbits with small numerical differences. This is another example showing that semiclassical.

关 键 词：心形台球 量子谱 定态展开方法 闭合轨道理论 混沌 

分 类 号：O562.3[理学—原子与分子物理]