BOUND STATES OF A CONVERGING QUANTUM WAVEGUIDE

We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 - epsilon, where epsilon > 0 is a small real parameter, i.e. the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + O(root epsilon). We will present a sufficient condition for the existence of a weakly coupled bound state below pi(2), the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when epsilon -> 0(+). RI Cardone, Giuseppe/I-2998-2012 OI Cardone, Giuseppe/0000-0002-5050-8908