In the quantum models described by analytic potentials $V(r)$ with several pronounced minima the phenomenon of tunneling opens the possibility of a sudden relocalization of the system after a minor modification of parameters. This may really reorder the minima and change, thoroughly, the shape of the (measurable) probability density. In the spectrum one observes the “avoided crossings” of the energy levels. By definition, the relocalization configurations are sensitive to perturbations and represent, therefore, a crossroad to alternative evolution scenarios. As long as the numerical search for these quantum analogues of the Thom's classical catastrophes is not easy, a systematic non-numerical approach is proposed here, based on an exact (or, better, quasi-exact) simultaneous construction of mutually consistent pairs of potentials $V(r)$ and wave functions $\psi (r)$.

在解析势所描述的量子模型中 $\mathrm{伏特}（\mathrm{[R}）$在具有几个明显的最小值的情况下，隧穿现象打开了在对参数进行较小修改后系统突然重新定位的可能性。这实际上可能会对最小值进行重新排序，并彻底改变（可衡量的）概率密度的形状。在频谱中，人们观察到能级的“避免交叉”。根据定义，重新定位配置对扰动很敏感，因此代表了替代进化方案的十字路口。只要不容易对汤姆古典灾难的这些量子类似物进行数值搜索，就根据相互一致的势能对的精确（或更好，准精确）同时构造，在此提出一种系统的非数值方法$\mathrm{伏特}（\mathrm{[R}）$ 和波动函数 $\psi （\mathrm{[R}）$。