 94323 P. Exner,P. Duclos
 CURVATUREINDUCED BOUND STATES IN QUANTUM WAVEGUIDES
IN TWO AND THREE DIMENSIONS
(97K, latex)
Oct 18, 94

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Abstract. Dirichlet Laplacian on smooth curved tubes in two and three
dimensions is investigated. It is shown that if the tube is
smooth and thin enough, and its curvature (and torsion in three
dimensions) decay sufficiently rapidly, there is always a bound
state below the bottom of the essential spectrum. A criterion
for existence of these bound states and an upper bound to their
number are derived. Furthermore, perturbation theory for these
eigenvalues with respect to the tube diameter is constructed and
some open questions are formulated.
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