用正则微扰理论和李变换法求经典一维四次方势模型的不变环面  

The approximate expression of toru for one-dimensional quadric potential model

作　　者：邢永忠[1] 曹文煜 

机构地区：[1]天水师范高等专科学校物理系,甘肃天水741001 [2]甘肃省机械工业学校天水分校,甘肃天水741001

出　　处：《西北师范大学学报（自然科学版）》2000年第2期27-31,共5页Journal of Northwest Normal University(Natural Science)

摘　　要：确定的动力对称代数的存在与否是人们最近所提出的判断给定的经典系统和量子系统是否可积的统一依据 .这一结论的得出是以超收敛级数为技术基础的 .作为除标准谐振子之外的第一个具体示例 ,详细地分析了一维含四次方势的经典模型 .分别利用一般的正则变换理论方法和超收敛级数技术求出了这一模型的哈密顿量与角坐标无关的近似表达式 .It has been demonstrated recently that the dynamical symmetry algebra is particularly suitable to characterize the integrability of both classical and quantum systems.An approximate expression of the Hamiltonian H(I) is obtained,which is independent on the angle variable,for one dimensional quadric potential model with the help of Kolmogorov superconvergent series.In order to show the advantage of this technique,the conventional canonical transformation and Deprit method are also used for the same purpose.

关 键 词：四次方势模型 正则微扰理论 李变换 不变环面 

分 类 号：O413.2[理学—理论物理]