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Bound States in Curved Quantum Layers

Pierre Duclos·Pavel Exner·David Krejcirik
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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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Pierre Duclos, Pavel Exner, David Krejcirik. 2001-02-27. Bound States in Curved Quantum Layers. https://doi.org/10.1007/pl00005582

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