Spectrum of the Magnetic Schrödinger Operator in a Waveguide with Combined Boundary Conditions
نویسندگان
چکیده
We consider the magnetic Schrödinger operator in a twodimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann1. We deal with a smooth compactly supported field as well as with the Aharonov-Bohm field. We give an estimate on the maximal length of the window, for which the discrete spectrum of the considered operator will be empty. In the case of a compactly supported field we also give a sufficient condition for the presence of eigenvalues below the essential spectrum.
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