Abstract.
We consider the magnetic Schrödinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann {For the definition of magnetic Neumann boundary conditions see Section 2, Eq. (2.2)}. 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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Communicated by Vincent Rivasseau
submitted 11/05/04, accepted 21/09/04
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Borisov, D., Ekholm, T. & Kovařík, H. Spectrum of the Magnetic Schrödinger Operator in a Waveguide with Combined Boundary Conditions. Ann. Henri Poincaré 6, 327–342 (2005). https://doi.org/10.1007/s00023-005-0209-9
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DOI: https://doi.org/10.1007/s00023-005-0209-9