椭圆量子弹道
chao-dyn
2008-02-03 v1 混沌动力学
摘要
研究椭圆弹道的精确量子力学与半经典量子力学。经典系统可积且存在分离变量，将阶段空间分为振荡运动与旋转运动的区域。经典的可分离性在量子力学中得以延续，薛定谔方程被证明等价于椭球波方程。量子本征值在经典行动空间中显示出清晰的模式。分离变量对波函数的影响予以说明。在存在分离变量的情况下，展示了一种考虑复轨道的统一WKB量子化方法，可用于半经典量子化。该方法良好地解释了能量空间中态的模式。我们提取出在能面上随能量平滑变化的有效Maslov相位，用于修正Berry-Tabor迹公式， resulting in a sum over non-periodic orbits. This modified trace formula produces the correct number of states, even close to the separatrix. The Fourier transform of the density of states is explained in terms of classical orbits, and the amplitude and form of the different kinds of peaks is analytically calculated.
引用
@article{arxiv.chao-dyn/9612020,
title = {Elliptic Quantum Billiard},
author = {H. Waalkens and J. Wiersig and H. R. Dullin},
journal= {arXiv preprint arXiv:chao-dyn/9612020},
year = {2008}
}
备注
33 pages, Latex2e, 19 figures,macros: epsfig, amssymb, amstext, submitted to Annals of Physics