等腰直角三角形的二维量子谱和经典轨道

Two-dimensional quantum spectra and classical orbits of isosceles-right triangular billiards

本文研究了等腰直角三角形中基于其波函数和能级结构的二维量子谱.虽然这个量子台球系统的本征态是无法分离的,但是关于两个变量的问题是完全可解的.通过对二维量子系统的波函数做相应的傅里叶变换,得到了系统的二维量子谱,把得到的结果和经典的二维量子台球轨道做相应性的对比发现:傅里叶变换的量子谱的峰值位置和经典轨道的长度之间存在着很好的对应关系,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.

The quantum spectra are derived from the wave-functions and the energy-functions of the isosceles-right triangular model. Al- though the eigenstates of the billiard system are not separable, the problem of functions with two variables is exactly solvable. The numerical results of the Fourier transform of quantum spectral functions are compared with the results from the classical orbits whose lengths match well with the positions of the spectra peaks. This result gives a new evident for the correspondence of quantum and classical mechanics.