01-79 Pierre Duclos, Pavel Exner, David Krejcirik

Bound States in Curved Quantum Layers (63K, LaTeX2e) Feb 27, 01

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Abstract. We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of geometrically induced bound states.

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