We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-integrable perturbation. The eigenstates change abruptly at avoided level crossing. After the avoided level crossing, they tend to restore their original form before the avoided level crossing, and exchange their distribution, especially for those which can be treated as isolated two-body collisions. But in general, the eigenstates have some changings after the avoided crossing, and the symmetries of the system are broken down locally at this kind of avoided level crossings.

中文翻译：

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哈密​​顿量本征态在避免的平交道口附近的行为

我们在数值上显示了哈密顿量本征态的变化作为控制不可积扰动强度的控制参数的函数。本征态在避免的水平交叉处突然变化。在避免平交道口之后，它们倾向于恢复到避免平交道口之前的原始形式，并交换它们的分布，特别是对于那些可以视为孤立的两体碰撞的。但一般情况下，本征态在避开交叉后会有一些变化，系统的对称性在这种避开的水平交叉处被局部破坏。