Bound States in Mildly Curved Layers

Details Bound States in Mildly Curved Layers Bound States in Mildly Curved Layers

2001-03-24

arxiv.org/abs/math-ph/0103032v1

J. Phys. A34 (2001), 5969-5985

Physics

Mathematical Physics

LaTeX 2e, 23 pages

Scientific paper

10.1088/0305-4470/34/30/308

It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can have bound states provided the surface is not a plane. In this paper we study the weak-coupling asymptotics of these bound states, i.e. the situation when the surface is a mildly curved plane. Under suitable assumptions about regularity and decay of surface curvatures we derive the leading order in the ground-state eigenvalue expansion. The argument is based on Birman-Schwinger analysis of Schroedinger operators in a planar hard-wall layer.

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