Bound States in Curved Quantum Layers

Details Bound States in Curved Quantum Layers Bound States in Curved Quantum Layers

2001-02-27

arxiv.org/abs/math-ph/0102033v1

Commun. Math. Phys. 223 (2001), 13-28

Physics

Mathematical Physics

20 pages in LaTeX

Scientific paper

10.1007/PL00005582

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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