Conditions for realizing one-point interactions from a multi-layer structure model

A heterostructure composed of $N$ parallel homogeneous layers is studied in the limit as their widths $l_1, \ldots , l_N$ shrink to zero. The problem investigated one dimension and piecewise constant potential Schr\"{o}dinger equation given by strengths $V_1, V_N$ functions l_N$, respectively. key point derivation conditions on $V_1(l_1), V_N(l_N)$ for realizing a family one-point interactions tend zero along available paths $N$-dimensional space. existence equations squeezed structure, solution which determines system parameter values, under non-zero tunneling quantum particles through multi-layer structure occurs, shown exist depend paths. This appears result an appropriate cancellation divergences.