可积系统规则运动的量子经典对应与有关问题  

Quantum-classical Correspondence of Regular Motion of Integrable Systems and Related Problems

作　　者：徐躬耦[1] 杨亚天[2] 徐鸣洁[3] 

机构地区：[1]南京大学物理系 [2]福建师范大学物理系,福建福州350007 [3]南京大学地球科学系,江苏南京210093

出　　处：《原子核物理评论》2001年第4期201-205,共5页Nuclear Physics Review

基　　金：国家基础性研究"非线性科学"资助项目;国家自然科学基金资助项目 ( 196 75 0 19)~~

摘　　要：基于表述经典及量子系统可积性的动力对称性群 ,对量子可积系统规则运动的经典对应问题运用归纳法进行了研究 .具体给出了经典近似描述的适用条件 ,并进行了简明讨论 .Based on the dynamical symmetry group characterizing the integrability of classical as well as quantum mechanics, quantum dynamics with proper initial conditions was genuinely formulated, and analytical solutions in the form of soliton-like state evolving around a certain invariant torus were obtained. It has been shown that, in case the intrinsic size of the evolving quantum state is significantly smaller than the extent of its evolving orbit, the motion can be satisfactorily treated with classical approximation. Having demonstrated the quantum-classical correspondence of regular motion, the possibility to study quantum chaos on the basis dynamical symmetry breaking was briefly discussed.

关 键 词：可积系统 动力对称性群 量子规则运动 量子经典对应 归纳法 量子力学 

分 类 号：O413.1[理学—理论物理]