Abstract:
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in ℝ3. 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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Received: 26 February 2001 / Accepted: 21 May 2001
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Duclos, P., Exner, P. & Krejčiřík, D. Bound States in Curved Quantum Layers. Commun. Math. Phys. 223, 13–28 (2001). https://doi.org/10.1007/PL00005582
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DOI: https://doi.org/10.1007/PL00005582