  We develop a general approach to study three-dimensional Schroedinger
operators with confining potentials depending on the distance to a surface. The
main idea is to apply parallel coordinates based on the surface but outside its
cut locus in the Euclidean space. If the surface is asymptotically planar in a
suitable sense, we give an estimate on the location of the essential spectrum
of the Schroedinger operator. Moreover, if the surface coincides up to a
compact subset with a surface of revolution with strictly positive total Gauss
curvature, it is shown that the Schroedinger operator possesses an infinite
number of discrete eigenvalues.
