Soft quantum waveguides with an explicit cut-locus

We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel fixed profile built along unbounded curve composed circular arc and two straight semi-lines. Using test-function argument help parallel coordinates outside cut-locus curve, we establish existence discrete eigenvalues. This is special variant recent result Exner non-smooth case via different technique which does not require non-positive constraining potentials.