For a 3D magnetic Schrödinger operator with potential on a locally deformed tube, the paper proves essential spectrum stability and gives an insufficiently supported sufficient condition for the absence of discrete spectrum.
Exner, Soft quantum waveguides in three dimensions, J
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Three-dimensional magnetic Schr\"odinger operator with the potential supported in a tube
For a 3D magnetic Schrödinger operator with potential on a locally deformed tube, the paper proves essential spectrum stability and gives an insufficiently supported sufficient condition for the absence of discrete spectrum.