二维圆环弹子球体系的量子谱分析

Quantum spectral analysis of two-dimensional annular billiards systems

基于自由粒子在二维圆形无限深势阱(弹子球体系)中运动的本征值和本征函数,计算了傅里叶变换的量子谱.把傅里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,发现傅里叶变换的量子谱的峰位和经典轨道的长度之间存在着一一对应关系,体现了体系的量子行为和经典行为的对应性.

Based on the energy eigenvalues and eigenstates,the Fourier-transformed quantum spectra for the problem of a particle moving in two-dimensional circular infinite well has been computed.By comparing the classical orbits and the quantum spectra,we find that the one to one corresponding of path lengths and locations of peaks is perfect,which testifies the relationship between the behavior of classical and quantum mechanics.