标题： 能量本征函数在经典禁戒区域上对无扰基态的收敛摄动展开 显示英文标题

标题： Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions

摘要： 我们研究扰动系统在未扰动可积系统的本征基上的本征函数的性质。 对于给定的一对扰动系统和未扰动系统，相对于每个扰动态的能量，未扰动基态可以分为两类：一类处于经典允许区域，另一类处于经典禁止区域；相应地，扰动态的本征函数也被分为两部分。 在半经典极限下，表明利用其经典允许区域中的本征函数分量，可以将经典禁止区域中的分量写成收敛的微扰展开式，该展开式适用于所有微扰强度。 显示英文摘要

摘要： We study properties of eigenfunctions of perturbed systems, given on the eigenbases of unperturbed, integrable systems. For a given pair of perturbed and unperturbed systems, with respect to the energy of each perturbed state, the unperturbed basis states can be divided into two groups: one in the classically-allowed region and the other in the classically-forbidden region; correspondingly, the eigenfunction of the perturbed state is also divided into two parts. In the semiclassical limit, it is shown that, making use of components of the eigenfunction in its classically-allowed region, its components in the classically-forbidden region can be written in the form of a convergent perturbation expansion, which is valid for all perturbation strengths.