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.