Pavel Exner, David Krejcirik
Bound States in Mildly Curved Layers
(71K, LaTeX 2e)

ABSTRACT.  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.