Emergence of a confined state in a weakly bent wire

In this paper we use a simple straightforward technique to investigate the emergence of a bound state in a weakly bent wire. We show that the bend behaves like an infinitely shallow potential well, and in the limit of small bending angle (φ≪1) and low energy-the bend can be presented by a simple one-dimensional δ-function potential, V(x)=-(2√c_bφ²)δ(x) where c_b≅2.1.