周期轨迹与不可积体系的量子化：Henon-Heiles体系的一个研究例子

研究了两个振子耦合的Henon-Heiles体系的周期轨迹与量子化问题.结果表明，周期轨迹的 作用量积分与体系的能量有着简单的线性关系.可以利用那些是整数值的周期轨迹的作用量 积分对不可积体系进行半经典量子化.由周期轨迹的物理内涵出发，揭示混沌体系的残余周 期轨迹具有与量子化有关的性质.这对于认识和理解经典力学与量子体系的联系关系及其物 理内涵有着深刻而重要的意义. 关键词： 周期轨迹 半经典量子化 混沌

Quantization of non-integrable Hamiltonian by periodic orbits: an example of the study on chaotic Henon-Heiles system

Action integrals of the periodic orbits of non-integrable (chaotic) two-dimensio nal system of Henon-Heiles were analyzed to show simple linear relations. This e nables us to obtain by extrapolation all the action integrals of any periodic or bits and at any energies from very few arbitrary action integrals. Based on this property, a very simple and easy semiclassical quantization algorithm by numeri cal arithmetics was proposed for low_energy excitations which are classically ch aotic. The result is good agreement with that obtained by the exact quantal met hod.