Local perturbations of potential well arrays

We consider an equidistant array of disjoint potential wells in \mathbb{R}^{\nu} , \nu\ge 2 , built over a straight line, and show that, under a restriction on the potential support aspect ratio, a perturbation consisting of longitudinal shifts of a finite number of them preserving the disjointness gives rise to a non-empty discrete spectrum below the threshold of the lowest spectral band.