Upper Bound for the Number of Bound States Induced by the Curvature of Singular Potential

We study a two-dimensional quantum system governed by the Schrödinger operator with a delta type potential. The interaction in our model is supported by a line Γ which coincides with a straight line at infinity. The aim of this paper is to derive a method which allows to find an upper bound for the number of bound states. The method presented here is based on the Birman-Schwinger technics. Finally, we express the mentioned upper bound in terms of geometrical properties of Γ.