Henon-Heiles哈密顿量的流动方程
Flow Equations for the Henon-Heiles Hamiltonian
摘要：
Henon-Heiles哈密顿量是在1964年作为一个数学模型引入的，用来描述星系中恒星的混沌运动。Delos和Swimm通过正则变换将经典哈密顿量转化为Birkhoff-Gustavson正规形，得到了离散的量子机械能谱。本工作的目的是首先将经典的哈密顿量对角化，然后使用不同的流方程，一种由Wegner在1994年引入的连续酉变换方法。通过流动方程对角化的结果是可比的经典变换所获得的。在相称频率的情况下，变换变得不那么冗长。此外，量子力学系统的动力学分析的基础上转换的可观测量。
英文摘要：
The Henon-Heiles Hamiltonian was introduced in 1964 as a mathematical model to describe the chaotic motion of stars in a galaxy. By canonically transforming the classical Hamiltonian to a Birkhoff-Gustavson normalform Delos and Swimm obtained a discrete quantum mechanical energy spectrum. The aim of the present work is to first quantize the classical Hamiltonian and to then diagonalize it using different variants of flow equations, a method of continuous unitary transformations introduced by Wegner in 1994. The results of the diagonalization via flow equations are comparable to those obtained by the classical transformation. In the case of commensurate frequencies the transformation turns out to be less lengthy. In addition, the dynamics of the quantum mechanical system are analyzed on the basis of the transformed observables.
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