Pierre Duclos, Pavel Exner, and David Krejcirik
Locally curved quantum layers
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ABSTRACT.  We consider a quantum particle constrained to a
curved layer of a constant width built over an infinite smooth
surface. We suppose that the latter is a locally deformed plane
and that the layer has the hard-wall boundary. Under this
assumptions we prove that the particle Hamiltonian possesses
geometrically induced bound states.