A heterostructure composed of two parallel homogeneous layers is studied in the limit as their widths l ₁ and l ₂, and the distance between them r shrinks to zero simultaneously. The problem is investigated in one dimension and the squeezing potential in the Schrdinger equation is given by the strengths V ₁ and V ₂ depending on the layer thickness. A whole class of functions V ₁(l ₁) and V ₂(l ₂) is specified by certain limit characteristics as l ₁ and l ₂ tend to zero. The squeezing limit of the scattering data a(k) and b(k) derived for the finite system is shown to exist only if some conditions on the system parameters V _j , l _j , j = 1, 2, and r take place. These conditions appear as a result of an appropriate cancellation of divergences. Two ways of this cancellation are carried out and the corresponding two resonance sets in the system parameter space are derived. On one of these sets, the existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac’s delta function, contrary to the widespread opinion on the non-existence of bound states in δ′-like systems. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.

在极限中研究了由两个平行的均质层组成的异质结构，它们的宽度为l ₁和l ₂，并且它们之间的距离r同时缩小为零。一维地研究了该问题，并且根据层的厚度，通过强度V ₁和V ₂给出了薛定equation方程中的挤压势。函数V ₁（l ₁）和V ₂（l ₂）的整个类别由某些极限特性指定为l ₁和l ₂趋于零。仅在系统参数V _j，l _j，j = 1、2和r的某些条件下，才证明存在于有限系统的散射数据a（k）和b（k）的压缩极限存在。 发生。这些条件是适当消除分歧的结果。进行这种抵消的两种方法，并得出系统参数空间中相应的两个共振集。在这些集合中的一个集合上，在紧缩极限中证明了非平凡束缚态的存在，包括以狄拉克德尔塔函数的导数形式出现的紧缩势的特定示例，这与普遍存在的关于不存在的观点相反类δ '系统中的束缚态。详细描述了单个绑定状态如何从有限系统中的有限数量的绑定状态在压缩系统中生存的情况。