Bound states of a converging quantum waveguide
We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − where > 0 is a small real parameter, the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + (√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below , the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when...